Chris, at that time in the IOM illegitimate children were usually known by the father's surname, even if his name wasn't given at baptism. So they would be under the father's surname in censuses, and in wills, or at their marriage.
Even when the father's name was given at baptism the IGI always puts the entry under the mother's surname, which is confusing but indicates an illegitimate birth. And this isn't how it reads in the register. The register usually has something like "John illegitimate son of .... and ..." - so is given no surname.

You can find the closest LDS Family History Centre (to order a film to view) in the phone book under "Church of Jesus Christ of Latter Day Saints".

The birth and burial entries you have been given come from Brian Lawson's indexes, and there is an explanation there of how they are arranged.
See: www.iomfhs.im/lawsons/births/_bir_index.html
and
www.iomfhs.im/lawsons/burials/_bur_index.html

See also wills at: www.iomfhs.im/lawsons/wills/_will_index.html
and
members.lycos.co.uk/ijradcliffe/

The numbers on the right-hand side of each entry are the LDS film numbers.

Sue