Gildor Inglorion was a Noldorin Elf of the House of Finrod. In The Lord of the Rings he met Frodo Baggins and his friends on the road out of the Shire. He warned him about the Black Riders, gave Frodo's company food and lodging for the night, and greatly impressed Sam.
The question has arisen of the identity of this character. Gildor calls himself "Gildor Inglorion of the House of Finrod." He also says: "We are Exiles, and most of our kindred have long departed and we too are only tarrying here a while, ere we return over the Great Sea.". At the time when The Lord of the Rings was written, Finrod still meant the character later known as Finarfin. If we read "House of Finrod" to mean "House of Finarfin", we can place him among the Noldor who joined the host of Finarfin during the Exile, and came to Beleriand under Finrod Felagund.
Some argue that the name "Inglorion", which means "son of Inglor" suggests, that he was in fact the son of Finrod Felagund himself, who was at that time still called Inglor. There is, however, strong evidence against it.
In The Silmarillion it is stated that Finrod had no wife, since he loved Amarië of the Vanyar, who refused to go with him to the exile. This means that he could only have a son after he died in Middle-earth and went to the Halls of Mandos. He might have been resurrected by Mandos, and then married Amarië. It is very unlikely (probably impossible), however, that he would be allowed to return to Middle-earth. The only such instance would be Glorfindel, and it is doubtful that if that was the case, there would be no mention of it in Tolkien's writings. Furthermore, Gildor wouldn't describe himself as one of the Exiles.
Also, if he were Finrod's son, he would have right to claim High Kingship of the Noldor instead of Gil-galad after Turgon's death. It is also said that there were only two children—Idril and Orodreth—of "the third generation from Finwë to go with the exiles."
It must be noted that when the name Inglor was abandoned for the character that would be Finrod, it is possible that the name reappeared, in Quenya form, for Finarfin (who in the earlier legendarium, was named Finrod). The essay Shibboleth of Fëanor mentions that Finarfin's full name was 'Finwë Arafinwë Ingalaurë'. If Ingalaurë is to be translated in Sindarin according to the sound-changing rules, this would become 'Inglor'.
It should also be noted that Tolkien initially used names from his (unpublished!) The Silmarillion writings rather at random in The Hobbit and the first drafts of the sequel which would become the LotR: other examples are the mention of Gondolin and the appearance of Elrond in The Hobbit, which were only later brought into alignment with the LotR and the unpublished mythology by a third edition of the book. It is likely that after realizing what the work had become Tolkien would have removed Inglorion as a name of Gildor, just like he intended to rename Glorfindel. In the end, neither of these changes actually were made.
This all suggests that, while Gildor might have been initially intended to be Felagund's son, in the final version he probably became a member of the House of Finrod as one of its servants, not one of its sons—perhaps one of the knights of Nargothrond, and a son of Inglor—a character unconnected to Finrod Felagund.