Imperial Princesses kept their Imperial family status after they married to men from non-imperial families, so they weren't identified themselves by their husbands' family names.
なお内親王は非皇族と結婚しても、本人の皇族としての身分はそのままであり、皇族を離れて嫁ぎ先の姓を名乗ることはなかった。