It does rather sound as if it was a bit of "D.I.Y." heraldry. That said, I can think of one possible reason for a name difference. If the daughter was heiress to her mother's Arms but not her father's. i.e. A man marries and has a son and heir. He marries for a second time a heraldic heiress and has a daughter. What I do not know is how the daughter would display the fact she is the heiress to her mother's Arms.
Using the combination of "the power of Google" and consulting other heraldry anoraks, it seems that the heiress displays her mothers Arms but with her father's Arms on a canton.
