Quoting Mama J♡:" So he was flirting with her. Still he knows he shouldn't be flirting with other women when he has a wife! that was premeditated. With full intentions to cheat, IMO"
This. You don't tell someone you want to kiss them if you haven't thought about doing it, and have no intentions of doing it. And the name? Really? I don't know if I would be more pissed about that or the cheating!
Would you be staying if he actually did cheat? What if he had given you an STD? Those were VERY real probabilities IMO.
Also, who knows what he was texting these girls and sending them over his phone? You said he keeps his phone locked up tight so you can never use/see it.