The real question is, Why?!
But yeah, Probably what everyone else has said.. If you're too awkward to ask (well, You cant be.. You're going to vlog in PUBLIC!) just try to be as sneaky as possible! OR record when you know nobody is around/looking.. Or at least, No staff members! Also, As long as the shop isn't displayed badly or if you just keep the name secret... Or something...
To be safe, ask, if you don't want too, don't.. Be a ninja.