Can't find my gt grandmother on the 1901 or 1911 censuses

[heywood]

Funnily enough Edwin Smith’s mother was called Rhoda Smith but they don’t seem to be connected.
His father was Benjamin and Rhoda Smith Teagle’s father was William according to marriage certificate.
I am so confused.

[brigidmac]

Re Teagle middle name
Could it have been given as a middle name to prove paternity
If he was born to a single mother the birth father would still have to adopt him to make him a legal son

Sounds like a case for DNA proof