Air Carrier on final for CLT overheard a company aircraft with the exact same flight number call for take off; the Controller was advised and made efforts to clarify subsequent instructions.

Narrative

On final approach to Runway 23 in CLT; and after checking in with the CLT East Local (Tower) Controller; we were cleared to land on Runway 23. At about 2.5 miles on final; we heard the same Controller issue a 'line up and wait' clearance to our flight; and it was acknowledged by another aircraft with the same/identical call sign as ours. Our flight was landing in CLT. The other flight was departing CLT. I immediately notified CLT East Local that he/she had two Company aircraft with the same/identical call signs. CLT East Local acknowledged my report with a surprised tone in his/her voice; stating 'yes; we do!' The Controller then issued the departure clearance to the departing flight as 'Company Departure.' After we landed; the Controller identified our flight as 'Company Lander' and gave us taxi instructions. Suggestions; tough call here. Dispatch should have been aware that our flight was almost two hours behind schedule. This delay triggered the dual call sign situation. An ACARS message to either crew or an Alphabetic suffix could have been issued to one of the flights.