Who makes logo designs?
A company that requires a logo design made for their brand usually approach a graphic designer.
A graphic designer is the person who uses his skill in designing to come up with various options of logos for your brand. They consider various components including what your brand sells, who is the target audience, what are the other competitors like, how big your brand is, what you expect from it etc.
They usually come up with a few options out of which you can make a final selection.
If a person wishes to do the job themselves there are many logo design creation, with download options available on the internet that one can make use of.