Are you talking about the conversation list or the quick reply pop-up? Or both?
I can only advise trying different message apps until you find one which does what you want. I just looked at Chomp, and in the conversation list that also shows the number, but in very small characters under the name (so may be a little better). Can't remember what Pansi does.
The stock messaging app on my phone just shows the name when in the conversation list, but as that's an HTC app you won't be able to install it on your phone.
Edit: Just checked images in the Play Store. These show numbers on both conversation and pop-up for Pansi, conversation only for Chomp, and neither for Handcent. So that would suggest that there is a setting for it somewhere in Handcent.