ZHU Controller; providing OJT; described a confused hand off event when I90 initiated a manual handoff on an aircraft that apparently had two flight plans in the system; the reporter suggesting I90 Controllers insure correct aircraft data before making a manual hand off and then relying on the ZHU Controller to make corrections.

Narrative

I was conducting OJTI (On Job Training Instruction) on Sector 49/86 combined with no D-side. I90 called with a manual handoff on Air Carrier X; departing IAH. My Trainee took RADAR on Air Carrier X and started a track using the /OK feature. After the data block appeared on our screen; my Developmental checked the flight plan readout and it indicated that Air Carrier X was actually an arrival to IAH. I was concerned that we had stolen the data block from Sector 84. After the Supervisor went over to Sector 84 to check if they had lost a data block; we figured out that Air Carrier X was on the downwind; landing IAH; inside I90 airspace. I then plugged into the D-Side position and called I90 and asked them to verify the call sign on the departure. He replied that he 'thought' it was Air Carrier X. I told him that there was already an Air Carrier X on their downwind. I90 replied with; 'Well that's what the Tower told me'. I instructed I90 to keep the aircraft; figure out his call sign and call us back. I kept investigating the issue and figured out that there was a flight plan on Air Carrier X departing IAH. However; it had not been DM'ed because of the other Air Carrier X. I called I90 back and told them what was going on. I told them they needed to change the call sign of one of the two Air Carrier X's and then DM the departure; and then hand him off to us. I told him that it was his job; and that we wouldn't be doing it. A couple minutes later; I noticed Air Carrier X (the IAH departure) in a southbound turn. I was then informed that I90 had shut off all departures because of this situation. A few minutes later; I90 apparently figured it out and initiated the handoff to us. Recommendation; I would recommend that I90 ensure that their traffic is squared away before they start making manual handoffs. I feel like they just let this aircraft fly along; knowing there was an issue; and then expected me (or my trainee) to fix it. That's not how it works. I don't know what the I90 Controller showed on his RADAR screen; but I'm assuming he wasn't able to have a data block on Air Carrier X (for the same reason I couldn't: there were two Air Carrier Xs). I feel that he should have taken steps to fix the situation before it got to me. And regarding I90 stopping departures; I never said anything remotely resembling 'Stop departures'. However; I believe that I'm being set up to take the fall for that. If anything; I believe I may have been a little rude or snippy to the I90 Controller. But that was frustration at him expecting me to do his job for him.