The shrink he saw was someone specializing in gender issues, so the shrink had a bias towards affirming Chris's gender identity.
It's odd that he never did it legally given how dedicated he is to the fantasy of being part Sonichu, it's about at the same level as his gender issues. Maybe it's because when he got his name/gender changed for the Christine identity, his gender shrink was there to walk him through the process. But unlike with trans stuff, there's no shrink that will entertain his delusion of being a Sonichu so he doesn't know how to navigate the name change process on his own.