After reading the thread on poop names, I did a search for pee names. The results are:-

Excitable Type
Pants are twisted, cannot find hole, rips pants in anger.

Sociable Type
Joins pals for a piss whether he wants one or not.

Timid Type
Cannot piss if anyone is watching, pretends he has been and sneaks back later.

Noisy Type
Whistles loudly, peeps over partition to have a look at the other fellow's tool.

Indifferent Type
All urinals being occupied, uses sink.

Clever Type
Pisses without holding tool, shows off by adjusting tie at the same time.

Vain Type
Undoes 5 buttons when 2 will do.

Absent-Minded Type
Opens jacket, takes out tie, pisses in pants.

Worried Type
Is not quite sure what he has been up to lately, makes a furtive but close inspection of tool while pissing.

Disgruntled Type
Stands for a while, grunts, farts, tries to piss, fails, farts again and walks out
muttering.

Sneaky Type
Drops silent farts while pissing and looks at the bloke next to him.

Sloppy Type
Pisses on shoe, walks out with flies undone, adjusts himself ten minutes later.

Learned Type
Reads a book or newspaper while pissing.

Childish Type
Watches bubbles at bottom of the urinal while pissing.

Strong Type
Bangs tool on side of urinal to remove drops.

Drunken Type
Pulls out tool, sees two, puts one away, and pisses in trousers.

Embarrassed Type
Covers tool with both hands and pisses through fingers.

Cock-Eyed Type
Stands in one cubical and pisses in next one