I was presented with a possible invention the way the person presented the product there were many problems. I went away and came up with a design that would work for his requirement. At no time did he pay for my design work or time. He has now filed for a patent under his own name as the designer. Can this happen as I have proof that I designed the product?
It's possible that he is the legal inventor, depending on the nature of the "problems" which you encountered. It is also possible that he isn't, and that you're the legal inventor.
The issue is going to be whether or not his "requirements" met the legal definition for an invention and didn't require any additional inventive steps. If the solution to these problems were "obvious to one skilled in the art", then your solutions weren't inventive.
I've been on both sides of this very issue. In the first instance, one of my earliest granted patents would have required that an engineer with ordinary skill select an appropriate set of components to implement what was disclosed. Nothing "inventive" would have been required, but any physical implementation would have involved tradeoffs. In the second instance, I was implementing a granted patent issued to a co-worker. I had questions about the patent, so I went upstairs and sat down with the inventor. Once I had a better understanding, I went off and implemented what was disclosed. In both of those cases it is possible someone who is unfamiliar with patent law might conclude the inventors weren't actually the inventors, but in both instances the patents were issued to the correct people.
It is possible, however, that what this other person "designed" was just an abstract idea and additional inventive steps were needed to overcome problems with the initial "design". You'd need to describe what you did in more detail here (which is a bad idea -- you could put the patent at risk), or contact an attorney who can help you understand if you should legally be the inventor. A more productive path might be getting that person to list you as a co-inventor and recognize whatever contributions you made -- it's possible you are both inventors in the legal sense.