Pseudonym

Hello everyone, I am new here.

I am nearly finished the first draft of my novel and was in the process of looking at potential agents and publishers. I am a closet writer (as I imagine most writers may start out that way!), so I do not want to use my real name on the finished worked. Do I need to legally do anything to go by my pseudonym or do I simply let the agent/publisher know this is the name that should appear on the cover? Also, do I need to write both my real name as well as the pseudonym or can I get away with writing just the pseudonym on my submissions? Any feedback is much appreciated.