Whenever looking at a re-registration it is so important to see both entries. The chain of events seem to be:
The birth in Dec 1943 is registered ( in Jan 44) by her mother. The inclusion of a maiden name (shown as "formerly") indicates she is, or has been, a married woman. There is no father named, so she didn't try and claim that her husband was the father , as she could have, although it would have been perjury if she knew it to be false. Unless the actual unmarried father was present his details couldn't be entered so the father's name is left blank.
In 1950 the birth was re-registered, with both parents present. The mother is using the father's surname but there is actually no way to be certain if the parents were married at that time just from the way the entry is worded. If the mother was already married in 1943 then even if this couple had married later the provisions of the Legitimacy Act wouldn't apply because at the time of the birth one of the parents (maybe both ?) were not free to marry. So the birth was re-registered as still to unmarried parents and both signed as informants.
There was no legal requirement for them to re-register the birth, it was something they chose to do presumably to ensure the father's name was recorded.
