Not necessarily. It'd be for how he views himself. While the shapeshifters kinda' explore the concept in some episodes, it may be fair to assume they identify as they present, because they can literally present how they want.

Granted, I could see Odo having some odd identity issues with presenting to please others or over duty to his job more than personal identity given his upbringing...

Did they explore his gender identity in that episode(s) or did they leave it all allegory? Ugh it was so long ago... Maybe time for a rewatch.