I'm not following the rules in the OPs video, and in fact, I find them borderline offensive. And I'll leave my fan fiction characters to one side, because none of you would know what the hell I'm talking about. So, using characters from established sci-fi, here's how I think I'd roll things together:
Admiral of Starfleet's Vela Halo Area Exploration Fleet: Admiral of the Fleet Lady Dame Honor Stephanie Alexander-Harrington
Our Hero Ship, attached to aforementioned fleet:
U.S.S. Vesuvius (reassigned from the Terran Confederacy Fleet from Wing Commander IV and updated with Starfleet tech).
Captain: Captain Morgan Bateson (naturally)
Exec: Commander Tigh (from
the original Battlestar Galactica)
Helm: Lt. Pilot (from Farscape)
Ops, 2nd Officer: Lt. Commander Allison Blake (from Eureka)
Security Chief: Lt. Kimberly Possible (grown, of course)
Tactical Officer: Lt. Alex Rogan (The Last Starfighter)
Chief Engineer: Lt. Commander Emmett Brown (Back to the Future)
Counsellor: Dr. Niles Crane (Frasier - yeah, not quite sci-fi, but I don't care.

)
Communications: Ensign See-Threepio (Star Wars)
Chief Medical Officer: Dr. Simon Tam (Firefly)
Ship's Chaplain: Vedek Kira Nerys
Ship's Computer: GlaDOS (from the end of Portal 2 -
not before 
)