Is it really common to say "I have a relationship"? I would instinctively say "I am in a relationship". Maybe though it is also because my mother tongue is German and in Germany people say "Ich bin in einer Beziehung".
My mother tongue is also German, so maybe I picked a wrong example for this :D A better one would be "I have a partner" maybe? I've read it some time ago, so I don't remember the exact examples, but you get the idea.