All the Bateman's on Island in 1881 appear to derive from John Bateman born in England - there is a family tree (very sketchy in IoM Fam Hist Soc J. vol 10 #4 but it was hand drawn and thus I did not scan it in.
John married Christiuan Milburn 1-Mar 1828 and had some 10 children in Lonan - the Eldest John married Issabella Brown and had 6 children (this family moved to Rushen) and one child married and moved to Fleetwood - very little info on any others is given
The name crops up in a mining context in my records (use search page on Manxnotebook- see top bar on page)
I have sightings of Manx Batemen's (not a Manx name) in US 1880 census - Ohio and Nevada (mining!)