You certainly shouldn't stress one over the other as this would sound strange. You should pronounce each with equal intonation- your voice should remain constant and equal over both names.

If you are introducing a friend to someone do you use their entire name? I usually will just say something like, "Oh I'd like you to meet Mary a friend of mine" or something similar. I think it would sound funny to use name/surname in that situation. In a business situation where you are introducing a new employee to everyone it might be okay to say, "Everyone this is Mary Smith she will be starting today in our marketing department".

I agree with Derrick. If it's a business situation then you should use both names but don't stress either one. If it's a purely social situation then I only introduce people by their christian (first) name.