You can probably guess my attitude to this: we should absolutely accept both of them!
Gilitīro is probably the most solid: was there a time when Celeborn was a Teler who was
not the grandson of Olwe? My understanding is the Telerin heritage all came as a single block. Since Gilitīro is a Telerin name, he would by definition be Olwe's son (or, possibly, the husband of Olwe's other daughter).
*Elulindo is more difficult. It would
probably still look the same in later Telerin; the name would be either Elue+Lindo (
Quendi and Eldar) or Elwe+Lindo (
Shibboleth), but I think Elulindo is the most natural combined form for either of those.
But would Olwe have named his son "Singer of Elu"? Some Amanyar elves (cough Finwe cough) liked to name their kids after themselves, so **Olulindo would follow from that, but that's a completely invented name at this point.
But... what if he was born after Elwe vanished? After Olwe had given up hope and was looking westwards again, or even had already left? "Singer for Elu" would be a way to memorialise his brother in the person of his son. So it's
plausible; and in the absence of any other information, I don't see any reason not to at least tentatively accept it.
You may recognise this as the same logic I used for
Maedhros, grandfather of Feanor, and Meril mother of Gil-Galad in the same thread. I just want them all to have names!
What we really need to support this as something
Tolkien might have intended is an example of him changing a direct relationship but keeping a more distant one. Gil-Galad and Celeborn both kind of did that: Gil-Galad jumped around the family tree but always remained a descendent of Finwe, while Celeborn's swap to being Telerin still kept him in the "grandson of Thingol's brother" position. So... we probably
can say that if Elulindo had been an actual character, he would have remained so as "son of the Lord of Alqualonde" even after that lord's name changed.
hS