Is there a reason that a proton has a positive charge while an electron has a negative charge? Are these just names that were given to the charges or was there a reason for making a proton have a positive charge?
There is no particular reason why one should be of such a sign and the other of the other. The choice is mostly historical and the opposite choice (positive charge for the electron and negative for the proton) would work as well with just some slight sign changes in the equations. The only important part is that their charge be opposites.
Protons are not an elementary particle, whilst electrons are. Protons are made up of Quarks, electrons aren't made up of difference constituent parts; they're just electrons. I'll leave it to you to look up the constituent parts of protons; they have individual charges within themselves.
The actual reason that one is positive and one is negative is slightly more tricky. If that's the answer that you're looking for you need to perhaps ask a more specific question.