Mr Happy asked "Does anyone know how this naming process evolved?"

Manchester = Mancunian

History of the name of Manchester - Wikipedia
The name Manchester originates from the Ancient Roman name Mamucium, thought to be a Latinisation of an original Celtic name (possibly meaning "breast-like hill" from mamm- = "breast"), plus Anglo-Saxon ceaster = "town", which is derived from Latin **castra = "camp".[12]

**[castrum - singular, castra - plural] Helen


Origin from Latin name of Manchester - Answers.com
Man·cu·ni·an (măn-kyū'nē-ən, -kyūn'yən) pronunciation
adj.

Of or relating to Manchester, England.
n.

A native or inhabitant of Manchester, England.

[From Latin Mancunium, Manchester, of Celtic origin.]

The Latin origins of Ceaster - Chester - castra also relate to Chester & Lancaster.

Chester = Cestrian

Lancaster or Lancashire = Lancastrian

Liver-"pool" to Liver-"puddle" => Liverpuddlian

Liverpool = Liverpudlian

I live in Newcastle in Australia. We refer to ourselves as Novocastrians from the Latin - nova = new & castrum = camp.

I don't know if the people from the UK city of Newcastle refer to themselves this way.

Helen