DA50 First Officer reports confusion over similar sounding fix names on the LANTK 1 arrival to OMA. The crew believed they were being cleared direct DSM (Des Moines) and it took three attempts and a phonetic spelling by ATC before the crew realized they were cleared direct DABOY.

Narrative

In cruise about 130 NM NE of DSM on vectors; Chicago Center cleared our aircraft direct to DSM (Des Moines VOR) and the LANTK 1 STAR into Omaha. The clearance was read back correctly as heard by both pilots. A few minutes later Center gave the clearance again '...direct Des Moines LANTK 1.' The clearance was read back as heard by both pilots 'direct Des Moines' again. The controller then immediately issued the clearance a third time; however this time clarifying the aircraft was cleared direct DABOY intersection LANTK 1; and phonetically spelled DABOY. The clearance was read back by the pilot and the aircraft flown to DABOY. Apparently the controller had been clearing the aircraft to DABOY intersection in previous clearances that the pilots had both understood as 'Des Moines.'Although this situation was corrected quickly; I feel there is a safety risk on the LANTK 1 arrival. 'Des Moines' and 'DABOY' sound very similar when listening through an aircraft radio in a normal; fast-paced context. Normally these two fixes are far enough apart to not cause confusion; but on the LANTK 1 arrival they are both transitions from the East and sound very much alike! I would suggest to change the name of DABOY to something different so there is no confusion in the future. Another contributing factor was the aircraft's original clearance which was DSM LANTK 1 OMA. Both pilots were expecting to be cleared direct DSM after vectors; not direct DABOY.