Do I need an agreement with my logo designer?
Yes. Just because you pay someone to create or design a logo for you does not mean you own the copyright or other intellectual property associated with the design or logo.
The creator of any material or image automatically receives copyright protection for their work when it is created, meaning they can sell it to any or all of your competitors or use it themselves.
Therefore, you must be given permission in writing to gain a monopoly on that image. Furthermore, the agreement should specify your right to register the logo as your trademark.