Lyric discussion by so_ein_pech 

Cover art for Daniel Cowman lyrics by Regina Spektor

Daneil Cowman is a shout out to Modest Mouse's Cowboy Dan. If you don't interpret Cowman as a last name, then they essentially have the same name. In MM's song Cowboy Dan is alive, but a part of that song links thematically with this one:

He drove the desert, fired his rifle in the sky And says, "God if I have to die you will have to die"

Regina matches this with:

On the day that Daniel Cowman stopped existing the world should've ended right then and there

So Regina is referecing Dan/Daneil's wish that the world end along with him. Given that Dan is a stereotypical name for a cowboy, it could all be a coincidence but its a cool idea anyhow.