As a name, it can be written in kanji:
http://ja.wikipedia.org/wiki/岩井俊二
However, it doesn't mean "celebration" there. It's like a "rocky well" or "muck well" or something odd. It should be treated more as "just a surname" (not a name to give a dog) than "a name that means something."
I can't say that I've ever seen the first as a name, but I have never lived in Japan with pets. I'd take a wild guess that since animal types (e.g., ネズミ rather than 鼠) are typically written in katakana, pet names would also be written in katakana. This is, however, a completely wild guess.