Last names in ME

[Legolas]

Legolas Greenleaf actually repeats itself - Legolas means 'Green-leaf.'

Elrond's 'Peredhil' is, as you said, just a title, denoting his half-elven ancestry.

Gil-galad's 'first name' can be looked at in the same way - a title, denoting ancestry. Ereinion means 'descendent of kings.'

Thorin's surname, Oakenshield, was not given at birth. It is more of a nickname, actually, which he earned at the Battle of Nanduhirion.

Bombadil's Elvish name, Iarwain Ben-adar, too, is a title - 'oldest and fatherless.' 'Tom Bombadil' was apparently given to him by Bucklanders, as Tolkien tells us in The Adventures of Tom Bombadil:

They also show that the Bucklanders knew Bombadil, (4) though, no doubt they had as little understanding of his powers as the Shirefolk had of Gandalf's...

Footnote 4, corresponding to the quote above:

4 Indeed they probably gave him this name (it is Bucklandish in form) to add to his many older ones.

In the case of Finrod Felagund, his surname, Felagund, was given to him by the dwarves (as it is Dwarvish, of course). They called him such ('hewer of caves') when Nargothrond was being carved underneath Taur-en-Faroth.

There in Nargothrond Finrod made his home with many of his people, and he was named in the tongue of the Dwarves Felagund, Hewer of Caves; and that name he bore thereafter until his end.