jmmoric,
You still terminate the transmission with the aircraft callsign, so ATC knows who is replying.
Remember (see Annex X, Vol. II) in this case the use of the call sign is the accepted substitute for "over" or "over and out", phrases that many current pilots would never have heard used.
Use of the "callsign" in this case should not be confused with the use of the callsign in initiating or responding to an initial pilot/controller contact.