A nick-name formation feature of English

simu

You add "s" to the end of a name or a part of a name e.g. Mary becomes Mares, Trinny Trins and so on. Anyone know what this is called and what the exact rules that govern it are?

hullaballoo

Heh, or hullaballs as Herr K used to call me.

is_that_so

The shortened versions you refer to here are just abbreviations of names.
They tend to come under an area of linguistics called phonaesthetics which deals with sounds and our preferences for them. Many abbreviations/nicknames are accepted in common usage( e.g. Bill, Willo,Trish,Paudge ,Pat,Tricia) whereas others are influenced by phonaesthetics - preferred sounds, so we can express a form of affection for someone through the nickname. Ultimately you are looking at an area of usage that is immensely fluid. As a result you are looking at the types of patterns people themselves prefer and also what is common within their own social groupings, which means that their choice of language will also be influenced by sociolinguistics.
This study which is a bit dense may help you. But like a lot of things in English usage you are reduced to analysing patterns.

simu

Good link there. Thanks, I'll have a read of it soon.

nesf

There are some interesting regional differences. The use of -o in Dublin Johno, Benidicto etc..

Cork generally uses y iirc. I can't remember any more off the top of my head.