Covering up the tattoo isn't about regretting your love for the guy, but about respecting the love of the new guy (if he wanted it removed). Crossing it out is just tacky.
Did you get the cross tattooed on it?, why not just fill it and and turn it into a picture of something, like flowers or something, the old name could just be the stems of the flowers
It's really interesting - over in the Love & Sex part of HF, you'd almost get flamed to a crisp if you said you were uncomfortable with reminders or even explicit discussions your lover's past, yet here in the Body Mod area the majority of opinions go the other way. I'm not saying one perspective is right and the other one wrong, just a little fascinated by the contrast. Personally, I think that I would be ok with it - maybe not comfortable at first, but eventually just fine. I think I would respect it for the gravity of what it represents while understanding that it's a closed chapter and not a threat. Otoh, if it causes problems for a partner, you may make have to decide which is worth more - the tattoo or the partner's feelings. Again, no real right or wrong, just whatever works.
i know a lot of people that have done this. when the name is a part of a design (like mama's butterfly foot prints), it's not bad, but when it's just a name...i don't really see the point. what, are you gonna forget the kid's name?! obviously everyone's children are extremely important to them. don't see how a name tattoo is necessary. even funnier than that - i know a girl with her OWN name tattooed...on her neck. "hello, i'm" *points to neck* "nice to meet you"
If I was the op's new dude I'd be all about getting that covered up, unless we was just messing around. But yeah, if things were serious, I wouldn't wanna be seeing your ex's name on you every time we got it on.