Okay so lets say i'm running Doom/jsa i play a moment of crisis and choose Dr. Doom giving all characters i control the identity Dr. Doom, now i flip up Doomstadt, Castle Doom, Characters you control named Dr. Doom get +3 atk. Do all characters i control with the identity Dr. Doom get +3 atk or do i not because they're identity is Dr. Doom not their name?

They need the name, not the identity.