It all sounds very odd from the little detail given.
As the mis-registering of details on the birth certificate would be criminal, the mother's details are nearly always correct, though the marital status might be fudged to show her as married when she was not. So she might be shown as Mrs Brown (ie, married to Mr Brown, the father), when in fact she was Miss White (ie, her maiden name).
But to have a completely different name, if that is what you are saying, registered at the baptism a mere 3 days later is odd. I had expected you to say the baptism was years later, which is not un-common. Why would the religious authorities allow a completely different woman to be shown in such circumstances ?
The possible solutions, and I admit to speculation here, that come to mind are :
1) Could this be an example of an informal adoption ? Formalised adoption does not come until much later.
2)Conicidence, so that there is a birth and baptism in close proximity with similar names involved. I have been confused by such events where cousins with the same first name were involved.