Can I register the name of an app before the app is finished?

I would also have a professional trademark search performed and analyzed by an attorney, because you want to know if the Mark is already in use by someone else before trying to file on it. Finding out now may save you a lot of money, time, and heartache.
Sometimes people pick Marks that aren't registerable. Talking to an attorney will let you know if your Mark is or isn't. Again, this will save your money, time, and heartache!

PS Filing your own application is not a good idea. But if you really want to, be sure and take the time to self educate before you do. Start with all of the USPTO Trademark videos and helpful articles for self filers at www.uspto.gov/trademark.

Hope this helps!
Mary

There is a distinction between your goods and the app with which people may purchase those goods. Use in commerce is a prerequisite for USPTO (i.e., federal) registration. If you have not yet used your brand name or logo ("Marks") in commerce with your "self-designed items," you may still file a Section 1(b) intent-to-use application. Your Marks will be examined for register-ability and whether such registrations would create likelihoods of confusion with preexisting registrations or live applications. If everything looks ok and your applications are not opposed, you may file a Statement of Use once you are using the Marks in interstate commerce, thereafter acquiring your registrations. To answer your last question, your Section 1(b) applications can generally act as a placeholder for your Marks, though your ability to ultimately register them will depend on others' preexisting uses of similar marks for similar goods. Your ability to use the Marks in commerce does not have to depend on whether your app is live (e.g., you could sell the goods over a basic website). The nature of your questions highlight that it would be very prudent to speak with a trademark attorney in private to evaluate your proposed brand name / logo and larger branding strategy (e.g., domains, social media handles, etc).

I am assuming your main market of interest is the United States, if this is the case I recommend you apply for the trademark in uspto.gov basing the trademark as "intent to use".

Regarding the application it is necessary to classify it in one or more of the 45 trademark classes. If you send me a list of what the app does I can send you the classification that corresponds to you.

Regards,