I'm almost publishing my game to Google Play, but I wonder if I can use an fake name, I mean, not using a fake name with a real names, just some words like Lazer Dude or anything else, because I don't want to show who am I, I wanna keep my anonymously. There's no problem to use an fake name?
You cannot hide your real name from Google. The distribution agreement you enter into is between you (or your company) and them, and they will require sufficient personal information from you in order to allow you to distribute (and in return, disburse your payments) that they'll be able to identify you.
The public-facing name you use doesn't have to be your own (as near as I've been able to tell), as long as you don't pick something that would be impersonating some other intellectual property or brand.
You can consider filing a DBA (doing-business-as) registration (or the equivalent outside the US). This is a fictitious name legally associated with your business entity (which would be a sole proprietorship in this case). It may provide some additional legitimacy.
You should consult a lawyer familiar with business law and practices to be 100% sure, as I am not.