The certificate was issued by the GRO, and the fact that it incorporates a photocopy indicates that it's a direct copy of the return submitted at the end of the relevant quarter - note the wording "a true copy of an entry in the certified copy of the Register...."
So this isn't Barbara's own handwriting, but a reproduction of it by whoever completed the return - and it looks like a pretty good attempt at that script. Because of the repeated pattern of letters in her name, it's possible that the extra 'b' appeared at the time of copying (it's missing in the name box above), so you'd need to check the original register to see how she did actually sign.