I see many fellow web builders call themselves interactive designer on their portfolio or in their email signature.
My humble word of advise: don’t.
The expression interactive designer does not make sense – you are a human, so you, me, they, we all are interactive in essence. Since all designers are humans(1), and humans are creatures of the “living” type, interactive per se, what you are really saying is closer to “i am a designer who does not master the English language very well”.
If what you want to convey as meaning is: “I design on an interactive medium. In so doing, i do not pursue to design interactions, but really, experiences: interactions with a content so that meaning emerges in the spirit of the beholder” then the words you were looking for are Interaction designer or, even better, user experience designer. I would then understand what you want me to understand, and so we would connect to each other on some mental meta level. Creating great user experiences is a beautiful mission, have at it.
Language is powerful, use it wisely.
1. “except God” would argue some (but not me).