It's not unheard of, though I don't run across it much. I think it's kinda cute, though. To me it's no different than naming a car or a pet. The guy's treating his member as a companion in adventure and enjoys having it around. I like my dick and have had lots of good times involving it, but I've never felt the urge to give it a nickname. To each his own.
With all the men who are into cock rings and other "restraining devices" - to each his own as far as that goes too
- I'm surprised there aren't any specially-made ID tags out there. They make 'em in all kinds of shapes to attach to pet collars, so why not have genitalia-shaped ones etched with the organ's "pet" name too?
I think it'd be hilarious to start in on a guy's male appendage and find a name tag swinging from the base.