Mara Omentie!!!! I little introduction: I read a lot of History of Middle-Earth in the early 90's, and learned elvish BEFORE the internet using the appendices and my trusty dictionary of Middle-Earth to translate EVERYTHING I could. I am fluent in Tengwar script and because my learning was very Etymological I might be able to help here. (AIYA! this site is incredible compared to how I used to learn)
(Edit Added vowel notaion): I speak Quenyan pretty exclusively so my translations are such. How this is in Sindarin or how the language changed in Sindarin I don't know :)
to start I can make a Quenyan meaning from Thilivérn quite easily, the problem is the pronunciation. The character Þ (TH) has a very complicated history, also Þ and T are not related in the Tengwar. T is from the first row: T>P and K>Kw while Þ is found in the third row TH(Þ)>PH and SH>CH (Rows matter a lot)
additionally, there was a mutation from primitive to modern elvish where Þ went from TH>S thus TH>PH became S>F in Exilic Quenyan. (This is directly mentioned in the Silmarillion as it changed Fëanor's mothers name from Therinde to Serinde and he didn't like the sound). that is why THIL=Shine it became the more recognizable SIL in Quenyan
And so Þilivérn in ancient would be Thilivérn, but modern Quenyan it is Silivérn. Which can be broken into Sili-Vére(n) translating to "Gleaming-Oath(I)" or put poetically "I, the Gleaming Oath"
the problem is you want the final pronunciation to be (tɪl ə vən) and the spelling doesn't work. EVEN if the elvish didn't soften to TH>S as mention TH and T are not related and evolving from one to the other is FAR from natural in an elvish sense. it would require the Archaic pronunciation of Thilivérn being taken by Westron speakers and hardening the TH>T through rules I have no insight on.
oh boy, that's long. hope it helps! anyone feel free to add or correct :) I am relearning after YEARS and only now with such wonderful resources