FAQ for
Galaxy Quest (1999) More at IMDbPro »

We only see Alexander away from a convention, appearance or the ship once, when he is in his apartment, on the phone to Gwen. It is likely since he is still wearing most of his costume that this scene takes place not long after he has gotten home after the convention, and simply hasn't taken the headpiece off yet.

While on the ship, he likely wishes to maintain the illusion that is really is Dr. Lazarus, so as not to confuse the Thermians.

Cmdr. Peter Quincy Taggart: Captain James T. Kirk.

Dr. Lazarus: Spock

Tawny Madison: Lieutenant Uhura

Tech Sergeant Chen: Chief Engineer Scott

Lieutenant Laredo: Ensign Chekov, Wesley Crusher

Guy, aka Crewman Number 6: the in famous "red shirts", one-off characters who would go down to a planet with the officers and be quickly killed by aliens, to illustrate the danger of the situation.

Wesley Crusher: Tommy Webber