Had a good friend go through this recently. They talked, she wouldn't come fully clean about important details like who wand what was said, he started watching things more closely. The relationship went downhill as she started turning his suspicion into him overreacting and being overbearing, several months later she did the same thing again with someone else. She was of the opinion (like several here, apparently) that sexting isn't the same as cheating and he should be okay with it since it didn't progress to physical, he wasn't okay with it. Her "position" is that he threw the relationship away over something inconsequential and that she wanted to be with him and just get the ego stroke of having others interested (like other said, this was positioned as a "You don't give me enough of this attention, so I'm getting it in other non-physical ways"), his position is that she knew it amounted to cheating to him and she promised to stop to save the relationship the first time and then went back on her word. They went from discovery of the first incident to divorce in about ~9 months.
Your wife needed something (the feeling "needed" comment is telling), she's getting it from another man rather than working with you, she knew prior to you finding out that it would cause issues so she deceptively changed the name to Katie to avoid suspicion, then when she was "caught" she went scorched earth on the evidence to avoid any specific accountability (and she can always deflect blame with statements like "YOU weren't giving me enough X" or "I told you it was nothing, why are YOU putting this stress on our relationship by questioning it, don't YOU trust me?"). For me, I'd require full honesty and openness and then work through whatever issues are there (and there ARE issues, otherwise it wouldn't have got this far). Given what you've shared, I don't have high hopes that she's really interested in the openness it would require for me personally to get past this sort of betrayal. if it's enough for you, that's something only you can decide. That you've posted here leads me to believe that you didn't get what you needed to repair the damage she's done to your trust. That's on her, don't let her deflect it to you. If she won't take responsibility and give you what you need to repair the damage to your trust, I don't see a happy ending for this marriage. Good luck.