Is suffixing a personal name with "-azza"/"-azzer" a standard Cockney nicknaming rule?

In two British films I recently recalled, I noticed a trend in nicknaming that I'd like confirmation of, by someone familiar with spoken Cockney English.

In the first one, Lock, Stock, and Two Smoking Barrels, I believe Barry the Baptist, an entertaining paid enforcer, is called Bazza or Bazzer either by his boss, or by those "two Northern monkeys", I can't remember which.

In the second movie, Layer Cake, I remember a guy, a member of a Cockney English-speaking drug gang, being referred to as Gazza basically throughout the entire movie.

My first question is : Is this a standard rule for nicknaming amongst Cockney English speakers? My second question is: If it's a rule, from what first name does Gazza come? My final question, the one I care about most about, is: If it's a rule, can I get some examples on how this rule would be applied to other names?

It's very common, but certainly not specifically Cockney. In fact, one of the most well-known owners of this nickname - footballer Paul Gascoigne, universally known as Gazza - is from Gateshead, in the north-east of England, about as far as it's possible to go from Cockney London and still be in England.

I'm not sure if it's specifically cockney, but it's a common transformation. It's mostly applied to an "ry" ending:

Gary -> Gazza

Jeremy -> Jezz or Jezza

Mary -> Maz (or Mazza, although that seems to only be applied in jest in my experience).