Yes, it's perfectly normal, and you should express your discomfort to your mother. Ask her to please back off from wanting you to call your stepfather “dad” and to respect your wishes. This is a situation where you need to stand up and do what's right for you. While she and your stepfather may feel disappointed at first, they'll soon get over it.
I admire you for not just “going along to get along.” In the short term, it would be easier to just cave in to their request. In the long term, though, it might eat away at you and cause emotional distress. It could feel like a betrayal of yourself.
Perhaps, you and your stepfather can come together and pick out a unique name for him that you both like. Get creative and have some fun with it.