The name Manchester originates from the Latin name Mamucium or its variant Mancunio. These names are generally thought to represent a Latinisation of an original Brittonic name. The generally accepted etymology of this name is that it comes from Brittonic *mamm- (“breast”, in reference to a “breast-like hill”). However, more recent work suggests that it could come from *mamma (“mother”, in reference to a local river goddess). Both usages are preserved in Insular Celtic languages, such as mam meaning “breast” in Irish and “mother” in Welsh. The suffix -chester is from Old English ceaster (“Roman fortification”, itself a loanword from Latin castra, “fort; fortified town”).

From wiki