While not really a name, I refer to my 09 3 HB as "the bus", since parallel parking it for the first time made it seem like one (mind you, I was driving a MINI Cooper prior to the Mazda, so anything would have seemed like a large, multipassenger vehicle).

The reference also helps prevent confusion, given that there is another Mazda (an 03 6) in the family.

 

My wife is now a proud owner of a Copper Red Mazda 3 Touring hatchback. She has named it Elizabeth, after Queen Elizabeth I.