Yep , we formed as Manchester City in 1894 , although we have actually been in existence under other names since 1880 ... namely St Marks(West Gorton) and Ardwick FC, but those early versions of what eventually became MCFC would still have attracted fans that stuck with us.
Likewise with United, who were initially formed as 'Newton Heath LYR' back in 1878 , by a scouser in a trainyard ..... they then later changed their name to Manchester United in 1902 ... but they would still have gathered support from their early days.