It is very clear that hearing OM's name is a trigger for you which tells me that you are not completely out of the woods yet. That alone should be the guidepost to your state of mind.
Let me tell you my experience that, I hope, would illuminate things a bit better for you.
Early on in my sitch, I could NOT stand the OW's name. It was like a finger going down slowly on the chalkboard. Also could not stand the sight of coming across a woman that looked like OW. I had murder on my mind. That warped thought process went on for several months (I am not going to lie and say "a few months"). Now? I no longer have that visceral reaction to the OW's name. It is more of eh...barf. Then it's over.
I managed to use my favorite tool a lot during the early months: duct tape. That was the one thing I really had to be dedicated to was watching my mouth (and fingers). The itch and antsy pansty feeling to react immediately to seeing and/or hearing hurtful things is what all newbies experience. You're still experiencing raw pain whenever you see or hear about OM/name. I get that. Totally.
The key thing is to manage your expectations and reactions.
As for the "lying" part, have you ever stopped to consider how and some of the ways you ARE NOT making W safe to confide in you without exploding or flying off the handle?
When you learn to manage your emotions, I bet W will be able to confide in you and come up to you more often when you calmly state, "W, this is very hard (painful...whatever adjective you insert here) to hear and I appreciate you being honest here by bringing it up to me. I need to take a brief time out (or take a day ...whatever time you need) to process this and will get back to you when I am more calmer."
This accomplishes several things. One is that you heard W. Two that you have this reaction. Three that you need time and will re-engage. This way, she will know that you will get back to her at some point instead of leaving her in the lurch guessing etc. This is called communication, my friend.