Ham is not what comes to my mind when talking bbq in fact ham is not what most consider bbq at all and many don't like ham, so ham is out, unless you want to stress smoked meats which is something different than bbq. Not really caring much for any of the names on the pole, and I would guess in your area you already have many businesses that use Motor City in there name, so it wont stick out in peoples minds. Go simple like what is your Dads name? You could take a back seat, and call it, fill in the blanks here,
__________ & Son bbq, just keep it simple.
Lg Spicewine on trailer
Weber charcoal grill
2 ugly drums, semi retired
Bbq toolbox, formerly Chargrill smoker
My wife has gas, its a Brinkman.