I'm not really a beer namer. I usually just stick to the style and include whatever hops were used for bittering. So I would have a "Chinook IPA" or a "Falconer's Amber Ale." I think it's kind of cool that people do name their beers though, especially those who have a special recipe they came up with. If I ever get to that point and come up with a signature beer, I'll probably start naming. Just as others have said, it's easier to remember "Titan IPA" than "Hey, remember that IPA you brewed and had on tap back in September, that was good."
That being said though, my brewery has a name. Heiserbršu. Basically it was a given that was going to be the name considering every one who tasted it for the first time, without any prompting by me at all, said, "Awesome, my first Heiser brew." So, that one just seemed pretty simple. So I do have a little logo on the top of my tap handles, above, "IPA" or "Amber Ale"