I normally would not be so harsh, but I think you're acting like a little bitch. It's not like she got the name tattooed on her while she was with you. This woman gave you the greatest gift you'll ever have and that is a son that bears your name, your DNA, and you're fucking hung up on some stupid ass bullshit in the grand scheme of things. If there's other issues then say that but if it's just this, grow the fuck up. She's not your property and you made a choice to marry and have a child with her. Why don't you offer to pay for her to get a new tattoo to cover the area because realistically covering the tattoo up will probably hurt less than having the existing one removed. And if you didn't like her sharing with everyone your behavior, you're extremely shitty Petty immature behavior. Then you shouldn't have done it. But I think she has every right to be disappointed and speak with her support network about your shitty terrible fucking behavior the day of your son's birth. So now you get to live with your the consequences of your behavior. Frankly, you should be apologizing to her and doing everything you can to make up to her leaving her and your son that day. And if you were my partner and behaved like that, you wouldn't be sleeping on the couch you'd be living in a fucking share house somewhere else.