As her birth certificate shows, Olive was illegitimate.

As in many such cases we may never know for sure who the father was.

JWK Stone was 26, single in the 1901 census.
I cannot identify Catherine or Olive in the 1901 census.

There may be all sorts of reasons why Olive used her mother's name. Her father may never have acknowledged her or there may have been some form of agreement that in return for financial support his name was not to be used. One could speculate for ever.

At her marriage she would have given her father's forenames but could have deliberately omitted his surname. The clerk could have assumed Cowley.

It may be worthwhile looking for Catherine & Olive in the 1901 UK census.