You use "may" for asking permission to do something. Better options for your question include: Could someone recommend me a movie? Could someone recommend a movie for me? Does anyone have any movie recommendations?

In this question you are requesting someone for a favor or help. The right way to ask this question is. Can someone recommend me a movie?

You would not use "may" here. "May" is used only when you need the other person's permission or consent. For instance, I *can* go to the bathroom (I am able to), but I *may* not go to the bathroom during class. "Can" is sometimes a grammatically correct option for a sentence like this, but when you are making a request, "could" is correct. Think of "could" as "can" + "would. The person CAN recommend a movie to you, but you are asking whether they would do it for you. Hope this helps!