I think it is likely that the three names are mentioned on the birth certificates and when the certificates were indexed, the staff were unsure which name was correct so they indexed all three. I have seen other instances of multiple indexes for the one certificate, usually based on spelling variations.
I may be wrong, and there may have been multiple registrations, but with a single ID number and year, I think this is unlikely.
I could imagine that the father on the certificate is given asHarry Grigson and the Mother is given as Elizabeth Ann Smith maiden name Kite.
If this was the situation then the children's name could possibly legally be Smith, but if she was a widow, divorced or separated from Mr Smith, she probably wanted the children's father on the certficate and you may need to find a marriage certificate for one of the children to determine which name they commonly used.
I think buying one of the certificates should resolve the name mystery.