Enroute Controller described operational deviation involving a descent clearance that was accepted by a similar sounding call sign aircraft in another sector's airspace.

Narrative

It was my last day of the week; so my start time was XA30. The sector was moderately busy with traffic; non-radar activity; and an aircraft on approach. The surrounding area was a bit noisier than normal - there were more people in the room due to bad rides up high. I was on a landline call when an aircraft checked on at FL290 descending to FL240. I believe it was ACR X; as this was the only aircraft in my sector at those altitudes. I answered the aircraft and cleared him to FL160 an issued the appropriate altimeter - this ACR X was landing. I believed I heard the correct readback. A couple minutes later; ACR X check-on. I told them that he already had checked on but he stated that he hadn't. I proceeded to give ACR X a clearance to FL160. I then transmitted in the blind trying to figure out who took the initial FL160 clearance. About 2 minutes later; I took the handoff on ACR Y flight who's datablock showed FL240 assigned; but the aircraft was at FL200. I believed another Center was taking the aircraft below FL250 traffic near the boundary and would be calling me to update the datablock. Receiving no call. I transmitted to see if ACR Y was on frequency. He was and stated he had been assigned FL160. ACR Y took ACR X's clearance and I did not catch the readback. Factors contributing were fatigue; noise; and workload. In addition; it is possible I would have been able to correct the situation if I would have recognized the problem sooner. 1) The other Center put ACR Y on my frequency without handoff. 2) I believe I was talking to ACR X when the sector above still was. I changed ACR X datablock and the sector above did not say anything.