I'm looking for a word that means "having the right to use this word."
For example, one could argue (and let's not argue whether or not this is true) that a gay person has some degree of agency/authority/word-I'm-looking-for in using the word "gay."
In general, this could be applied to derogatory terms, where the people against whom they are used have the right to "reclaim" them.
I don't know of any word that refers specifically to jurisdiction over words. I might say, to use your example, that gay people have a 'claim' to the word 'gay.' Though 'claim' does have some of the sense of legislated rights, I think it can be used without that meaning interfering. I might also use the word 'entitled,' as in "gay people are entitled to use the word 'gay'" -- although this word comes with a connotation of 'undeserving,' it literally refers to having the title to the word in question (again, 'title' may be more related to legislated rights than what you're going for.) 'Prerogative' might also be useful here, as in 'It's my prerogative as a gay person to use this word to describe myself.'
I think this would depend on the history. In the case of "gay" it was originally (as I understand it) a deniable code word: "When I asked if he was gay, I just wondered if he felt happy and carefree. Perish the thought I meant anything else!". Later it moved into common usage and became a synonym. Hence "appropriated" would seem sensible, as FumbleFingers suggested in the comments.
In the case of words with a pejorative history, like "nigger" or "queer", it seems that the affected sub-cultures have deliberately used them to take the moral high ground from the enemy. But I don't know any good words to describe that process. "Reposessed" or "seized", perhaps?
Link to the wonderful song "Taboo" by Tim Minchin
I believe the best word would be "Reserved". Similar to the above video, there are words that are acceptably used in the average vernacular only by those of that subgrouping. It's not wholly based on sexual preferences or race (while the aforementioned words 'queer', 'Jew', 'white trash', 'nigger', 'cracker', & 'gay' all would certainly fall into that category) as you could include more socially normed terms would fall into that category.
Using House of Cards as an example (reflecting respect to real life presidents) Claire Underwood calls her husband "Francis", his friends call him "Frank", but those names are reserved for them - in any other context, to any other character he is Mr. President, or simply President Underwood, because they aren't allowed those reserved words.
Likewise, my children call variations of "Father" (including Dad, daddy, et cetera), but that term is reserved for them - Everyone else my proper name, or some variants thereof.
Something similar happened with the distinctions of people with disabilities. While it was, at one time, in the vernacular to refer to 'cripples', the 'deaf', the 'dumb', the 'retarded', that has since been swept away - first it was banded together with the umbrella word 'handicapped', then each individual group decided which word they wanted to use their own. The general word, even used by international consortium, is 'disabled people', but even that is being rebelled against recently with 'differently abled'.
