Enroute D-Side Controller described a confused hand off event when accepting RADAR on a VFR target when in fact the hand off involved an IFR aircraft requesting climb; the event resulting in an airspace incursion.

Narrative

The neighboring Center called for a hand off. There was a VFR aircraft flashing at us that was close to the boundary; so I picked up the line and said RADAR. He didn't give a call sign in the coordination. The RADAR pulled up a target that was in on the boundary; and it was flashing to Sector 21. The RADAR /ok the Data Block; and the aircraft checked on. The RADAR flashed the aircraft to 86; looking for higher. Sector 86 dialed in and said there was no flight plan information; just as we had made the discovery there was no flight plan information stored in the NAS. Point out was made to T45 with an explanation that it would be a few minutes before he would climb; we were trying to get flight plan information put in. The aircraft had reached FL230; and was requesting FL280. I unplugged from the D-Side; plugged into the Sector 84 D-Side; and passed flight plan information to the T43 Sector so we could get the aircraft climbing. I recommend that when calling a sector for a hand off; you use the call sign for identification. I realize I could have asked who; however coincidentally there was a VFR aircraft flashing to us 2 minutes from the boundary; and I assumed it was that aircraft. I also recommend that when initiating a hand off; address it to the correct sector; and don't wait until the aircraft is 30 seconds from receiving controller's airspace before coordination.