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).
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
" " = Important Work, * * = Author
( ) = Translations, _ _ = Regions
> = Direction of flow
*Quennar i Onótimo*
"Of the Beginning of Time..."
"The Tale of Years"
*Rúmil* | "Parma Culuina"
"Annals of Aman"---<---| _Doriath_ |
"Ambarcanta" | "The Grey Annals" |
"Ainulindalë" | | |
| | | *Pengolodh* | *Dírhaval*
|--------->-----+----->----"Quenta Silmarillion"--<--"Narn i Chîn Húrin"
| | |
| _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 Lord of the Rings")