The person who gives the adhan is called a muadhdhin.    From Wordnik.com.  [Archive 2008-03-01] Reference

The Sunnah (practice of the Prophet) recommends that while the adhan is being called, one should listen attentively and repeat it silently after the muadhdhin, but when he says “Hayya ‘ala-s-Salah” and “Hayya ‘ala-l-falah” one should say.    From Wordnik.com.  [Archive 2008-03-01] Reference