Yes, you can publish two apps with very similar (but not identical) names. It shouldn't affect your existing app (except perhaps sales and/or confusion on the app store on which version to download).
This seems to be the same topic as your other thread*...but it may be about more than just the name.
If the apps are different and the names are different, then as chuck notes you can go ahead...however - are the apps in question the same, otherwise? Do they do the same things with the same features?
Also, if they are, is it important to keep the same users?