I am going to create a new app (domain, name or anything?)

I am planning on making this app universal, and I have a basic question.

How is the procedure of legal things? How do I make the name of my app legal? Like mine.
How do I avoid getting legal problems with X country if they have my name already.

I don't really know where to post this so... Thanks in advance.

The biggest and most obvious one should be to stay away from trademarked (brand)names.

You could do a quick search for US trademark here: http://tmsearch.uspto.gov/bin/gate.exe?f=tess&state=4804:ru2jhe.1.1