Hey there, there is no way to check. By default, users have 3 name changes available to them - doesn't matter if you weren't playing during the time each was granted.
Name changes are currently unavailable. This is an issue that arose when Episode: Revenant launched.
This is a different issue to the one where players whose names were changed unnecessarily in August. Bungie has tried to unlock those names, but this has not worked for everyone. So the choice there is to keep waiting or go with something different (once the above issue is solved).
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For future reference, what are the limitations on the name change characters? It doesn’t explain what they are in the profile settings and I’d like to save us the trouble of me returning to the forums