Anyone born as a prince or princess into the Royal Family is born surnameless; this is why both of the princesses previously used ‘York’ as a stand-in for a surname. They don’t have maiden names as such.

We also cannot be sure that either princess has adopted the surnames of their respective husbands.

I imagine that those who become prince or princess by the accession of a grandparent might also become surnameless (in their sovereign grandparent’s realms) but am not sure.