I really love this name, not only because of Tim Burton, but it's also a great alternative to the name Robert. I have so many Robert's in my family, and instead of using Robert for my child's name, I could use Burton, since it has the same Burt/Bert factor. I love it!
In the U.S. it peaked in popularity in 1920 (249th position), but it is now out of fashion. To me, it sounds more like a surname than a first name and I'm not really a fan of this name. Despite the so-called Bert/Burt factor, it sounds similar to the more hideous grandad name Bertram.
I don't like the long vowel sound in the first syllable, and I really don't like the nickname Burt. This is quite an old-fashioned name, and it sounds like a name that doesn't suit young people to begin with. Bah.