How do you choose a strong startup name?

Just be creative and find something that fits.

I do homebrewing. My wine is Almost Moonshine Wine with the motto It ain't fine wine, but after two glasses you'll think it is, since it's usually 18%. My beer is Better Beer with the motto It's better than nothing... probably, because it's decent beer but sometimes I screw it up (self deprecating is probably not a good strategy for most start ups).