Y'know I don't think the Fawlty Towers link is going to be as strong, or even evident at all amongst this child's peers. They will "look" at the name with a relatively fresh viewpoint. John Cleese is a fairly well known celebrity for us but he wont be forever. My name was partly inspired by a "Big" movie of 1969 and partly my family heritage. I am finding that it's only generations of my age or older (I'm 41) who even remember the name in the movie. We all like to believe that our generations Pop Culture icons will be the enduring ones... but only a few of each generation remain... this I'm sure will work in this names favour. Afterall nobody let Aunty Jack (1970's TV comedian) put anyone off calling their child Jack!

ETA: oh and Baz is short for Barry too.