This seems like a confusing question to me. Pretty much every time I play I know who the alpha dog is. Often it is me, but I play with a couple folks who take that role when we play.
Basically it seems to me that the better I have gotten it has become clearer to me who should take each ball ... and on the tweeners that either player could take, the alpha dog takes control.
Pretty much the only time I say something other than mine is when I chose to let a ball go that would have been a difficult poach for me. If this is a relatively easy ball for my partner at the baseline that would allow him to move forward I will say "come up". But other than that, it is pretty much always "Mine" or "ME".
"You should be playing linebacker, not singles."