Air Carrier departure from MDW on Runway 22L questioned takeoff clearance because of aircraft in position on Runway 31C with similar flight number; resulting in a 'cancel takeoff' instruction from Local Control.

Narrative

While taxiing to Runway 22L; another aircraft with similar call sign was given line up and wait instructions on [Runway] 31C. We were then given takeoff clearance from Runway 22L as we approached the hold short. The transmission was slightly garbled due to radio interference; so my First Officer read back the entire clearance which included our flight number; our runway; and our turn instructions clearly and precisely to make sure of no miscommunication. We then made our required call outs stating the runway and clear in both directions. I felt uncomfortable knowing that there was another aircraft in position on the intersecting runway and with the multiple radio transmissions covering each other. I knew in my heart that we were cleared to go; but I wanted to make sure that everyone was on the same page. I asked my First Officer to confirm that we were cleared to takeoff from 22L. When he did this; Tower responded with a stop instruction; we stopped. Then Tower gave us position and hold. Then Tower gave the other aircraft takeoff clearance and shortly thereafter; gave us clearance to takeoff. Preventive measures: less general aviation traffic in congested areas and heads-up given for similar call signs.