The singer-turned-actress, who married Laurence Fox last year, said that the matching 'Mr Fox' and 'Mrs Fox' tattoos they got to commemorate their wedding are "vulgar".
Piper told Marie Claire magazine: "It's disgusting. We were in Mexico and both so drunk. I think we both regret it now. The thing is, I just look at it and think, 'God that's vulgar.' I don't know what I am going to do about it."
Talking about her refusal to take Fox's surname after they got married, Piper added: "Laurence was like, 'If you want to call yourself Billie Piper Fox, that's grounds for divorce'.
"Also, I really admire a woman who takes her husband's name and gets rid of her maiden name, but I can't for work. It reminds me too much of my dad. And I think a double-barrelled name is a bit w**ky."
Piper and Fox have a 15-month-old son called Winston.