What is the deciding factor for using "gaer" or "aer" in Sindarin names?

Hello! My question would be: what is the reasoning for using "gaer" or "aer" in Sindarin names (meaning sea)? As in, there is the Sindarin name Aerandir, however, the Quenya Eärendil is translated as Gaerdil (among others but all those start with gaer- as well); how come? What is it that makes the one with the “g” the correct one – would Aerdil not be accurate, too? It’s something similar with the Telerin word for sea as well gaiar or aiar but I read on Tolkiendil that Eärwen’s name in Telerin may be Aiaruen not Gaiaruen, because of the aesthetic? I’m confused about this… What is the deciding factor for using “g” or leaving it out? Or is it because sea in Sindarin is also "aear" which is then easier to say as gaer?

This may help some gaear.

Most Neo-Sindarin writers use gaer when used in a compound. Words that start with -g- it usually vanishes when attached to another word due to soft mutation.

From Eldamo: Voiced Stops (b, d, g): The soft mutations of voiced stops b, d, g are voiced spirants such as v, dh, except that g vanishes completely: i ’aladh “the tree (galadh)”. For clarity Tolkien sometimes marked the lost g with an apostrophe ’, but this is not required and has no affect on pronunciation. This mutation is a result of the sound change whereby voiced stops became spirants after vowels: v, dh, ʒ (IPA [v, ð, ɣ]); later on the voiced velar spirant ʒ (IPA [ɣ]) vanished. This mutation is extremely well attested, and applies even to consonant clusters beginning with voiced stops, as in ’laur the soft mutation of glaur “gold(en)” (UT/253). Welsh has the same mutation except [v] is spelled “f” and [ð] is spelled “dd”; Tolkien established the soft mutation of voiced stops all the way back in Gnomish of the 1910s (GG/7). Some examples from Sindarin:

beleg “great” → veleg (RC/536). dínen “silent” → dhínen (WJ/333). gaear “sea” → aear (LotR/238; PE17/27).

Thanks, though these soft mutations are complicated to me. So, it doesn't matter, for example, if it's Aerion or Gaerion, both are equally correct and means the same?

Your welcome. Yeah mutations are one of the more complicated parts of Sindarin, but after awhile you get used to them.

For Aerion and Gaerion they could be the same, but one could be misinterpreted as using S. aer adj. “*hallowed, holy”.