Bro, is this even real? This sounds so far fetched to even believe. And if it is real why do you have to ask us what to do about it? I mean how do you feel about your wife getting a full first and last name tattoo of another man on her ass for you to look at for the rest of your life?
This story is insane. I think we are being trolled on here now. There is absolutely no way I would ever be okay with my wife getting another man's name tattoo on her ass, especially just because she was bored. Come on dude. What does that say? I mean what does that tell you? At the very least it is extremely disrespectful to you. And at the most she is having sex with him and putting his name on her body is a sign of saying that her ass belongs to him.
What was another man doing at your house spending time alone with your wife while you were out of town? That right there should tell you even more. There is now way that is happening even if they are just friends. It opens up the door to so much more inappropriate behavior and feelings developing and talking about things they should not be talking about with each other and complaining about you and next thing you know they are having an affair.
And what does it take to work up to the point of them deciding to go get this done while you are gone anyway? What state of mind were they in? Were they under the influence? If so you can all but guarantee there was some hanky panky also taking place while you were gone. Was this a sober decision? Then I would be even more concerned. How does a wife make this decision sober? And if she was drunk then why was she drunk alone with your best friend at your home while you were out of town? Both of those scenarios are unacceptable.
Also, she did not think you would like her putting your own name on her body but you would be okay with her putting another man's full name on her ass permanently? That would be okay? This is not even real life right now brother. Come on. This has to be a joke.
Finally, are you ready for the nail in the coffin? Here it is: Her explanation about why she did it tells you everything you need to know. "She had been feeling neglected and alone so putting his name there made her feel wanted and needed because he is such a good friend." In what world is this even remotely close to being a normal reaction to feeling neglected? A normal rection would be to talk to you about those feelings if in fact she was even having those feelings at all in the first place.
The more likely explanation is that she is already starting to re-write the narrative of your marriage and frame things in such a way so as to explain why she and your best friend are so close and spending so much time together and to soothe her own conscience about what they are doing behind your back.
On top of all this, she refuses to address your concerns, refuses to take a lie detector, and refuses to have the tattoo altered.
Bro, what benefit of the doubt is there to give her? You are in denial if you think this can be explained away as them being bored. This is a deal breaker 100% of the time. Ain't no way in hell this is happening on my watch.