Can someone suggest if there was a general rule of thumb to follow of illegitimate children who, in the early 1700's were baptised with their mother's surname... did they later take on the name of their father?

Reason for query...I have a few Qualtrough illegitimates of this time period who I am finding difficulty in tracking down because they were baptised with their mother's surname then they disappeared....

Comments welcome.

Thank you.

Elizabeth