"I hope you have a good day!" or "Have a good day!" are the correct ways to say it. "I wish you a good day" is not a natural expression. If you have any more questions about English, do not hesitate to ask me. Kindest regards, Josh italki Community English Tutor

Are you talking about choosing a name for a baby? If so, you would normally say, "Have you chosen a name?" (We usually use the present perfect, "have you (done something)," in cases where you have to perform the action, and the question is whether you've done it YET or not. You have to name your baby, so the question is, have you already chosen a name, or will you choose one later?) If you're talking about choosing a name for someone or something else (and you are not obligated to choose that person's/thing's name), then you should use the form, "Did you choose a name?" You can also say this if you're talking about choosing your own name. Using "did" sets the action definitely in the past, and implies that whether or not you chose a name, the action is completed. In any case where you HAVE to choose a name, though, it will sound more normal to use the present perfect form. "Have you chosen a name for your company?" (If you have a company, you need to name it.) "Have you chosen a name for the character in your book?"

If you mean the question in the title, it would be "Did you choose a name" because in question you need to declinate the auxiliary verb, which is 'do' here. You only declinate the main verb if there is no auxiliary verb, which is very rare, if not non-existent.