What rights do I have over my domain name?

I bought a domain name about two years ago for a little web app I've been working on. For conversation sake lets call it Umize. Recently, a new startup launched with a similar name (Umizr).

Here's what bothers me: they use my name (Umize) as the title of one of their features. And this title is displayed prominently on their front page and throughout their web site. The feature is also somewhat related to my web app.

My question is: do I have any copyright for the use of my domain name? Do I have the right to ask the startup to rename their feature?

I'm not planning on taking any action now. I'm just wondering what my options are if this becomes a problem in the future.

Thanks so much!