My brothers father might be my father but my mother was having an affair with my brothers father with a guy called mark which is my middle name and I'm ginger and also mark is and my brothers father has dark hair so does my brother, but my mum keeps telling me that me and my brother share the same father but if she knew that then why did she put my middle name mark which is the name of the guy that she was having an affair with, so can me and my brother have a dna with out the suspected father's knowing?

You and your brother can have DNA testing that can determine the possibility that you came from the same father or not.

First... red hair is a recessive gene. It can occur no matter what the parents, grand parents or even great grand parents hair colors are.

Second... who do you expect is going to pay for this...

Third... why don't you ask the "suspected" father...

Forth... what do you expect is going to happen either way?

Fifth... How old are both of you? (this actually does matter)

Yes you both can be tested but what difference would it make?

None of the physcial things make any difference, brothers with the same father and mother can look totally different, that is how DNA works, so of course his hair and other things can be different.

She may have liked the name Mark, One of my boys name is Christopher, from a actor on TV, because my wife liked the name.

You are guessing at things.

But yes, if you are 18 and have the money, you can go get a DNA test done, to determine.

You two can find out if you are brothers or not - that's all. Without the father or possible father's DNA, you won't know who is the father.
I think you can get it done unofficially for about $100 (US) each.
Many places online will send you a swab kit.

What do you plan on doing with the information regardless of what the information is? I'd encourage you to have a plan in place for whatever you find out. A tread cautiously as well.