I've read the many places in England that end with "chester" were originally roman camps.
Also I see caster (Lancaster), xeter (Wroxeter,Exeter), cester (Glocester,Worcester) (maybe more?).
My question is: Who gave them these names?
These places all seem to have longer and different Roman names. For example "Colchester" in wikipedia is listed as: "Camulodunum" and "Colonia Victricensis".
I assume these were Romano-British place-names that stuck around after the Romano-British were overrun, but how come the variations? And how come there are so many of them?
'-chester' evolved from the Saxon word 'ceastre', which is an evolved form of the latin word 'castrum', which meant an encampment or a fort. Places where the Roman army had a permanent base or a fort often grew to become the established cities of the medieval world.
In regards to Camulodunum: that name is a latinization of the celtic name for the hillfort that stood there. 'Dun' is the Celtic word for a hillfort, while 'Camulos' is thought to be the name of a deity. So in that way, the old name isn't so different from the new name: it still denotes a fort of some kind.
Chester and caster are the Anglo-Saxon variations of what in French is "château", in Flemish "kasteel", in Spanish "castillo" and in Italian "castello": castle, from the Latin "castrum".
As you can see in the French version the sound "k" has turned into "ch", just as you have in "chester". This is quite common among Germanic variations, which Anglo-Saxon also is. Note for example the French "cheval" for the Italian "cavallo", or the French-speaking Swiss city of Neuchâtel (essentially a variation on Newcastle).
Romans tended to Latinise what was already there rather than create new names.
I assume these were Romano-British place-names that stuck around after the Romano-British were overrun, but how come the variations?
Variations are normally down to where the name is recorded, and how many iterations it's gone through. To give an example the city of York starts out as Eβορakov via Ptolemy, Latinised into Eubaracum/Eboracum. By the end of the Roman period, the 'b' became 'v' so the Angles altered it to Eferwic (c897) to Euorwic (c1150) replacing the 'ac' with 'wīc* (town). After the Scandinavians took it in 865, they adopted the name but mangled it through their own language(s) and so it became Iorvik > Iork, ʒeork, ʒork and finally York by the 13th century.
Carlisle starts off as Lugavalio, a personal name meaning 'as strong as the god Lugus' (a celtic god), but morphs by the 9th century into Luel, to which the old Welsh 'cair' (city) was affixed, so we get Carleol by 1108, Cairleil by 129 and thus Carlisle.
London on the other hand went through hardly any change - Londinium > London.
Caster as others have pointed out is a Latin word borrowed by OE. Bede suggests this when he says that 'the city of Rutubi Portus, which the English corrupted into Reptacaestir' (he has some other examples as well).