I haven't really noticed people being given rhyming nicknames in the UK (I'm a Brit), but it's pretty common for guys to be called by their last name (or an abbreviation of it), at least by other guys, anyway.
Having said that though, last year when I was doing my MSc, my friends gave each other nicknames that were unique to our friendship (i.e. we were the only people who used those nicknames for each other - no one else had a clue what they signified). Actually, also when I was about 10, my younger brother gave me a silly nickname that just kind of stuck - my whole family still calls me by the nickname 15 years later (even my aunt who lives on a different continent!).