One of the reasons he wanted to go see who was impersonating him was because he was angry. The other was because he was worried. As far as he was concerned, there could only be two types of people who might impersonate him: either a friend, or an enemy!
If it was a friend, he might still be angry, but would still need to determine who it was, and why they were doing something so stupid. If that person was still alive, and deserved saving, then he would save them.
If this person was an enemy... then he still wanted to know who exactly it was!
Furthermore, he was confident that after all the spirit enhancements his mask had received, it was definitely powerful enough that a demigod wouldn't be able to see through it. As long as he didn't slip up accidentally, no one would be able to determine his true identity.