From Twitter's Help Center [1]:
You may:
* Name your website, product, or application with something unique. Uses of Tw-, and Twit- are generally okay with us.
* Feel free to include language on your site explaining that your application is built on the Twitter platform so people understand your product.
* Use Tweet in the name of your application only if it is designed to be used exclusively with the Twitter platform.
You may not:
* Use Twitter in the name of your website or application.
* Use just "Tweet" or "Tweet" with a simple letter or number combination (for example, 1Tweet, Tweet, Tweets).
* Register a domain containing twitter (or misspellings of twitter).
* Apply for a trademark with a name including Twitter or Tweet (or similar variations thereof).
* Use Tweet in the name of your application if used with any other platform.
So the use of 'tweet' in an app name is allowed, if the app is a pure twitter client (not an app that integrates multiple social networks). You also have to agree not to trademark the name, if that name contains the word 'tweet'.
[1] http://support.twitter.com/articles/77641