ZHU Controller reported an unsafe condition involving helicopter operations in the Gulf Of Mexico suggesting improved radio coverage and the elimination of similar callsigns.

Narrative

As the on job training instructor I heard trainee issue Helicopter XXX clearance to HUM maintain FL050 and code with the read back garbled and broken due to frequency problems. Due to traffic that was off route and trying to get corrected for weather reconnaissance; (block FL050B060); I suggested FL040. When trainee issued FL040 to Helicopter XXX; I heard a different voice advise stand by. Then; I heard Helicopter XXY departing. Apparently we had both Helicopterr XXX and Helicopter XXY answering the clearance and SIMILAR CALLSIGNS FILED FROM SIMILAR RIGS AT SIMILAR COORDINATES. However; coordinates were stated in the clearance and they are not the same coordinates. The end result; Helicopter XXX was outbound VFR/065 and Helicopter XXY was inbound at FL040. This could have ended in an accident if both helicopters had been at their rig and departed at the same time. Recommendation; PLEASE GET THE GULF OF MEXICO GOOD FREQUENCIES WITH GOOD COVERAGE AND GET HELICOPTERS TO USE NON SIMILAR CALLSIGNS; ESPECIALLY IN THE SAME AREA; SAME COORDINATE AND SAME RIG BLOCK AREAS!