-Could you explain your situation a little more?
I'm sorry took so long for me to get back to you was away and could not get a connect to a laptop where I was. With all of the evidence you have so far it could very well be that he is either cheating on you or contemplating doing so, if he is willing to hide little things like that from you then he is trying to hide something even more incriminating from you and you need to tell him that you know her real name because you texted her and she confirmed what you believe to be the truth and that his continually lying to you doesn't help him to gain your trust but makes you trust him even less than you did when you first found out about this woman. You have to make a choice to either accept that what he is telling you is the partial truth and choose to believe him or believe what the evidence is telling you and decide if you want to stay or leave him. If he isn't willing to be honest and come clean that you can only assume that he is cheating until you get concrete proof.
If he becomes more distant or secretive then this could be a sign he is cheating on you. If you feel the communication is breaking down between he and yourself and he doesn't have much to say to you then this could also be a sign of a cheating spouse. If he spends a lot of time on the Internet without any special interest in a game or hobby he pursues on the Internet or leaves the room to take phone calls and even goes outside to take the phone calls, it could mean he is talking to his lover or other women in chat rooms on the Internet or in emails or on the phone. To know if he is cheating on you, you could check dating web sites and see if you can find him on there. Also if he discontinued the phone bill going to your home then that is a very good sign he is hiding something from you. The classic signs are there and you have to let him know that you will not put up with such behavior and that he needs to come clean or you will leave if he cannot tell you the truth about everything. If he gets really defensive that could mean that he is truly trying to hide something and try to make you think it's all in your mind but you have proof.
It's up to you to decide what you want to do with the proof you already have and the classic signs he is showing you. If he doesn't change then I would suggest making plans to leave if he cannot respect you and your feelings then that will not change just because you found out about him. Maybe try talking to the female and see what kind of relationship they actually had, either way you have to get answers and then decide what you want to do.