Trade name v.s. business name v.s. trademark

Ok here's goes, I'm in the process of establishing a business within the State of Maryland. My business name is not my name but it's a fully spelled out acronym of three words. It is not fully registered yet. Yet I see information that I also need to specify a trade name. So I guess my question is do I have to specify a trade name or can I just use my business name. My situation is similar to this example below.

I'm registering my business name as...

International Business Machines LLC.

However I will commonly use the following within documents etc...

IBM, L.L.C.

In addition I see that I need to register a trademark. I did some quick search and found that the trademark that I"m intending to use does not exist. So I guess my trademark is simply the logo that I intend to use that represents my business correct?

Thanks