Unless and until you're actually selling something (or trying to establish some sort of brand identity for other reasons), I wouldn't worry about it. Think about it? Sure, why not. But there's no reason that it can't change with every batch since there's not much need for a continuous identity.
For the occasions when I make labels, I have a little name and logo for the "brewery." It's a joke/running theme between a couple friends and I, but it wouldn't survive the transition to a commercial operation (there's already a moderate-sized brewery using the name). That doesn't matter, though, it's really just a fun design element to make the label look like a real product. Anyone who's talking about the beers I brew calls them my beers, not "xyz brewery" beers.
There's no reason not to have fun with it, but I'd start using a name when I happened to find one I liked. Until then, I'd just go without one.