It is possible for one child to be registered twice.
If a child is born to an un-wed mother, then the baby will usually be registered with the mother's name. If both natural parents later marry, the child can then be re-registered with the new married name of the couple. Step-fathers can't register as a father for this purpose, only the actual father (unless they lie, of course).
This can cause, as you may guess, serious confusion for us amateur genealogists.
I am un-clear if this is the case here. You may be able to tell by checking the dates of birth against the date the two births are registered and seeing if you can find a wedding involving the mother and father between the dates the child is registered.
Also, beware name coincidences.