Should I go out with a guy that doesn't want me to tell anybody that me and him are going out

Chances are he has a valid, if only to him, reason for keeping it secret. Ask him about it. Let him know you you feel, but figure that out first. Men typically need to here the important stuff in the first sentence or two, since after that they are distracted, either processing what they have already received, or something else.
Don't judge his response, listen and discuss it. Respect him and validate his feelings, even if they don't makes sense to you, they do to him. It could be that helping him process whatever is causing him to want to keep it secret will help him trust you, and your judgment of who it is safe to talk about the relationship with. It is very possible he has been burned by someone before, and that kind of pain has to be processed, not buried or ignored.

One possible reason could be concern about age difference and appearances. Is he older by chance?

obviously there is something wrong with this relationship if doesn't want anyone to know so no don't go out with him. He is not even worth it.

if it was me I would but hurt and upset and confused to why he didn't want people to know!

you need to ask him why because personally I think its something to wary of

Hell no! If a guy wants to keep you a secret then he doesn't deserve any type of relationship with you. He's basically saying you're good enough to chill with in private, but not good enough to be seen in public. That's not cool - you deserve better! You would be playing yourself if you went out with him. Guys who keep you a secret just want to use you for their own selfish reasons.

Well.you should ask him why he doesn't want you to tell everybody. Ask him if you can tell some of your best friends, and then he can tell some of his best friends. But don't break a good relationship because he won't let you tell anyone. Not trying to be rude at all but maybe he doesn't want you to tell anyone because he is scared his friends may laugh, trust me been there done that. good luck I hope my advice helps.