I really don't know much about copyright law (and I knew you weren't planning to name a rose after Aunt Millie), but I just have memories of ludicrous lawsuits. Spike Lee, for example, sued the Spike network on cable TV a few years ago for using his name even though the network's programming consisted mainly of adult cartoons and wrestling shows and had nothing to do with Spike Lee's films or philosophy. And Jimmy Buffett routinely sues anyone taking the name "Margaritaville" in vain.
Buffett probably does have a case because he has a chain of restaurants with that name, but what made Spike Lee so arrogant? When I hear the name "Spike," I'm likely to think of a dozen other people and even a bulldog before I think of Spike Lee.
A restaurant near my house opened with the name "Zuzu," but had to change it to "Zazu" shortly afterward, so someone apparently has a copyright on that name.