Vtyjkyuk

Did Tolkien ever say why Gondolin was so-called by its Sindarin name, instead of the Quenya: Ondolindë? Thingol forbade his people from using Quenya or responding to people who used it, as a response to the actions largely due to the Fëanorians, but the Elves of Gondolin, part of whom where Sindar, were led by Turgon, a Noldo, and obviously had no contact with the rest of Beleriand. If I remember the timing correctly, the move by Turgon's people from Nevrast to Gondolin happened after the ban on Quenya, but I find it peculiar that Turgon didn't maintain the Quenya name of his kingdom. Clearly history is written by the dominant group etc etc, and almost everyone else was speaking Sindarin in the outside world, but Thingol wasn't around (or around for long) to enforce the name change once Gondolin became known to the rest of Beleriand.

It is said that Turgon appointed its name to be Ondolindë in the speech of the Elves of Valinor, the Rock of the Music of Water, for there were fountains upon the hill; but in the Sindarin tongue the name was changed, and it became Gondolin, the Hidden Rock.

Aside from everything having multiple names in at least two languages, is there an in universe reason, or something from a letter explaining why the Sindarin name stuck?

Tolkien, a Translator

As I've stated previously, Tolkien envisioned himself, and the world around him, as part of Arda, and was therefore not an author creating a world, but a translator of histories written before him. The texts you read in The Silmarillion and The Histories of Middle-earth are translations (of translations) of the histories of Middle-earth recorded by the lore-masters of the Elves, Bilbo, Frodo and others. Given the likelihood that that these texts were translated from Sindarin to Westron/Old English, this is the likely reason for the use of the name Gondolin surviving to the modern day.

_{A map of the order works were written in, and the how the works influenced others will be provided at the bottom of this answer.}

Pengolodh and Ælfwine and early versions of the Legendarium

Pengolodh (Q. Quendingoldo/Quengoldo) was the greatest lore-master and chronicler in Middle-earth. Being born in Turgon's Nevrast, Pengolodh, of both Sindarin and Noldorin descent, migrated with the host to the hidden city of Gondolin. The Quenta Silmarillion was written by Pengolodh, although it is unclear whether he had written it in Sindarin or Quenya, it seems reasonable to guess that it would've been Sindarin, based on it being the common language he shared with the Teleri (the main inhabitants of Tol Eressëa). Furthermore, the recording of his name it its Sindarin form, seems to suggest a preference for the language in the recording of the histories.

Pengolodh, an Elf of mixed Sindarin and Noldorin ancestry, born in Nevrast, who lived in Gondolin from its foundation. He wrote both in Sindarin and in Quenya. He was one of the survivors of the destruction of Gondolin, from which he rescued a few ancient writings, and some of his own copies, compilations, and commentaries. It is due to this, and to his prodigious memory, that much of the knowledge of the Elder Days was preserved.
_{War of the Jewels - Quendi and Eldar: Appendix D}

For before the overthrow of Morgoth and the ruin of Beleriand, he collected much material among the survivors of the wars at Sirion's Mouth concerning languages and gesture-systems with which, owing to the isolation of Gondolin, he had not before had any direct acquaintance. Pengolodh is said to have remained in Middle-earth until far on into the Second Age for the further-ance of his enquiries, and for a while to have dwelt among the Dwarves of Casarrondo (Khazad-dum).
_ibid.

Ælfwine (Eriol), an English-man who had found his way to Tol Eresseä around 900 AD, was the latest translator of the works, and it was him who'd brought the works or the tales back to Britain. Ælfwine spent what may have been years on Tol Eressëa learning the tales taught to him by Pengolodh and at some point had translated the Quenta Silmarillion. It is again unclear whether he'd learnt Sindarin or Quenya, however as before it is likely, due to his being on Tol Eressëa, that he'd been taught to read the Sindarin writings of Pengolodh and learnt to speak Sindarin. As such, his translations into Old English would likely have preserved the Sindarin name for Gondolin.

These histories were written by Pengolod the Wise of Gondolin, both in that city before its fall, and afterwards at Tathrobel in the Lonely Isle, Toleressëa, after the return unto the West. In their making he used much the writings of Rumil the Elfsage of Valinor, chiefly in the annals of Valinor and the account of tongues, and he used also the accounts that are preserved in the Golden Book. The work of Pengolod I learned much by heart, and turned into my tongue, some during my sojourn in the West, but most after my return to Britain.
_{The Lost Road and other Writings - Quenta Silmarillion}

Bilbo's "Translations from the Elvish"

During the time of The Lord of the Rings, Tolkien's histories were (again) in turmoil. Ælfwine likely remained a part of the stories, however as opposed to him being the source for the Ainulindalë, Valaquenta and the Quenta Silmarillion, that task seemed to have fallen to Bilbo. In the Red Book, Bilbo had included the "Translations from the Elvish", which were known to contain at least the Ainulindalë and the Valaquenta and likely contained the Silmarillion. In this case, Bilbo was known (and Elrond) to speak Sindarin. In this version, it would've been clear that the name Gondolin would've been used in Bilbo's translations, as Elrond would likely have recorded the events in his native Sindarin, and if the texts were written in Quenya, the speakers of the Old tongues that Bilbo had around him would've translated into the Sindarin for him.

Quenta Silmarillion was no doubt one of Bilbo's Translations from the Elvish, preserved in the Red Book of Westmarch.
_{The Complete Guide to Middle-earth - Quenta Silmarillion}

and he gave him also three books of lore that he had made at various times, written in his spidery hand, and labelled on their red backs: Translations from the Elvish, by B.B.
_{The Return of the King - Book 6, Chapter IX: Many Partings}

But the chief importance of Findegil’s copy is that it alone
contains the whole of Bilbo’s ‘Translations from the Elvish’. These three volumes were found to be a work of great skill and learning in which, between 1403 and 1418, he had used all the sources available to him in Rivendell, both living and written. But since they were little used by Frodo, being almost entirely concerned with the Elder Days, no more is said of them here.
_{The Fellowship of the Rings - Note on the Shire Records}

This map is taken from the excellent resource The Chroniclers of Arda

Key: 

" " = Important Work, * * = Author 
( ) = Translations, _ _ = Regions 
 > = Direction of flow

 *Quennar i Onótimo*
 "Of the Beginning of Time..."
 "Yénonótië"
 "The Tale of Years"
 *Rúmil* | "Parma Culuina"
 "Annals of Aman"---<---| _Doriath_ |
 "Ambarcanta" | "The Grey Annals" |
 "Ainulindalë" | | |
 | | | *Pengolodh* | *Dírhaval*
 |--------->-----+----->----"Quenta Silmarillion"--<--"Narn i Chîn Húrin"
 | "Lammas"
 | |
 |----------------<-------------------+
 |
 |------------>--------+--------->--------+
 | | |
 | _Númenor_ _Rivendell_ 
 | "Indis i·Ciryamo" "Books of Lore"
 | | |
 | | |
 | _Arnor and Gondor_ |
 | | | *Bilbo Baggins* 
 | "Book of the Kings" | "My Diary"
 | "Book of the Stewards" +-("Translations from the Elvish")
 | "Akallabêth" |
"Quentalë | *Torhir Ifant* | *Frodo Baggins* |
Ardanómion" | "Dorgannas Iaur" | *Sam Gamgee* |
 | | | |----->----"The Lord of the Rings" |
 | | | | | |
 | | | | "The Red Book of Westmarch"
 | | | | *Findegil* |
 | | | |-->--"The Thain's Book"------<------|
 | | | | | [Many copies] _The Shire_
 | *Ælfwine* | | | | "The Tale of Years"
 ("Quenta Silmarillion") | +----------->----------| |
 ("Annals of Aman") | | |
 ("Grey Annals") | | |
 | | | |
 +-------->------------|-------------------<----------------+-------<-------+
 |
 *J. R. R. Tolkien*
 ("The Hobbit")
 ("The Lord of the Rings")
 ("The Silmarillion")

The Noldor had arrived to Middle-earth after the First Kinslaying, and when Thingol learnt of the latter he banned the use of Quenyan throughout his realm. This rule took place many years before Turgon sent his people to live in the secret valley, and so The Silmarillion says that the Sindar refused to use Quenya, and the Noldor adopted it into their everyday speech.

However, when Tuor first arrives at Gondolin, he hears:

And even as the echoes died in the stone, Tuor heard out of the heart of darkness a voice speak in the Elven-tongues: first in the High Speech of the Noldor, which he knew not; and then in the tongue of Beleriand, though in a manner somewhat strange to his ears, as of a people long sundered from their kin.

_{Unfinished Tales, Of Tuor And His Coming To Gondolin}

Further reinforced by a side-note accompanying the chapter:

In The Silmarillion nothing is said specifically concerning the speech of the Elves of Gondolin; but this passage suggests that for some of them the High Speech (Quenya) was in ordinary use. It is stated in a late linguistic essay that Quenya was in daily use in Turgon's house, and was the childhood speech of Eärendil; but that 'for most of the people of Gondolin it had become a language of books, and as the other Noldor they used Sindarin in daily speech'. The Silmarillion: after the edict of Thingol 'the Exiles took the Sindarin tongue in all their daily uses, and the High Speech of the West was spoken only by the lords of the Noldor among themselves. Yet that speech lived ever as a language of lore, wherever any of that people dwelt.'

Finally, in The History of Middle-earth:

His (Earendil) names were, however, given in Quenya; for Turgon after his foundation of the secret city of Gondolin had re-established Quenya as the daily speech of his household.

_{The History of Middle-earth, Book 12, Peoples of Middle-earth, The Shibboleth of Fëanor}

In-universe

Gondolin, to the other Elves, was known as Gondolin. Thingol's ban on Quenyan was taken seriously throughout Beleriand. However, within Gondolin itself it was called Ondolindë — his kingdom, his rule.

Out-of-universe

The Silmarillion used the Sindarized form of Ondolindë probably to prevent confusion to readers throughout the book. Constant switching between Ondolindë and Gondolin would have been hard to read. Even though Quenyan was still used within Ondolindë, its usage in Beleriand had severely dropped, even after Thingol's death.

It would stand to reason that it would be more appropriate to write a book in a language that is still used and understood by majority of the people, instead of a language that had, in the past, been shunned and now, is mostly forgotten.