I usually go with "The Pale Horse". While not "technically" a flagship, as I cannot myself pilot it (Usually a Rampart or mod-similar cruiser/capital class Exploranium AI ship), it is my main champion called upon to most all major fleet engagements.
Per mythology, the Pale Horse is Death, slaying all, with Hades following behind him with jaws open to receive to the afterlife all that the Pale Horse kills.
Unsurprisingly, I follow through with the other 3.
My main fuel hauler (usually a Prometheus or if using faction mods some capital-class tanker) is the Black Horse. Bringing fuel to bomb planets, thus bringing famine, as the horse should.
My main cargo hauler (again, either an Atlas or a faction-mod capital freighter) is the Red Horse. I tend to use AIRetrofits and build out a droid army for all my raiding / Nex invasion efforts, thus bringing the machine equivalent of like 4000 marines to wage war, as the horse should.
My main carrier is the White Horse. Kitted with wings upon wings of wasps, they are about as close to pestilence as you can get.
Thinking about it now, I guess I have been derelict in my RPing. I should name another cargo hauler Hades, to properly receive the "dead", in the form of supplies, metal, weapons, etc.