Hi Liz,

Cath could have been - like dozens of other children - registered under her single mother's surname with no father recorded. This is always a possibility which should be checked.
In the Isle of Man these children were often known by the father's name in later records, even when he wasn't recorded at birth. This was definitely not illegal (and still isn't today).
So you need to list all Cath births for possible years, including underage, of all surnames where only the mother was given. - And then keep this list to refer back to, and to compare with other information you gather. You might find some familiar-looking names amongst the illegitimate births.

Sue