How do suicide hotlines trace your phone number and send help to you?

I called a suicide hotline form my cell phone and I made sure that I wasn't home. So I drove somewhere and called from there from my cell.. And I get home a few hours later, and my house is surrounded by police cars and one ambulance. How did they track down where I lived ? I only told them my first name.. I was never asked where I live, or anything. So how was all this done ?