I think it's a very amusing name for a dog or rabbit but for a human, feel v dated and also reminds me of Brian the Snail from the Magic Roundabout and also The Life of Brian and also Bad Sir Brian Botany.
I know it's a personal choice but when there are so many lovely names it seems hard to lumber a baby, child, adult with a name like this unless of course you are naming after a Brian in which case a middle name?