There are instances where the mum may not have known which chap was the father of her baby and would therefore not be able to name anyone.
Whether an unmarried mother knows who the father is is not really relevant when it comes to birth registration - if she isn't married to him, he doesn't get shown on the birth register unless he is there with her to sign as co-informant.
I have seen quite a number of cases where no father is named on the birth certificate of an adopted child, but the actual adoption papers give all his details.
I have an instance in the 1960's in Wales where the mother obviously didn't know who the father was and therefore he wasn't named anywhere! Not on the baptism,birth cert or adoption papers.
I'm just pointing out that it is another scenario that you have to be prepared to encounter.
Hi ,'how on earth do you come to that assumption because she did not name the father?
To me it's not one bit obvious!
Perhaps the mother did not want the father named - not because she didn't know who he is, perhaps because she did not want him making decisions, ( there are a multitude of reasons!). You are assuming she did not know the father just because she did not name him .
Kind regards