Dunno about the colonies, but in England surnames weren't fixed at birth and there was no box for surname of child on the birth cert.
It's not valid to say they were registered with their mother's name just because the father's name is missing.
Of course they'll be indexed at the registry under the mother's name, but the index is only a finding aid.
Either the father's name or the mother's maiden name or the late husband's name would be valid choices - whether the father's name is registered or not.
Unmarried fathers weren't registered unless they attended in person, which of course wasn't usually convenient during office hours.