Ethiopia is the proud birthplace of coffee. Coffee there is drunk ceremoniously, and to be invited to the house of an Ethiopian for coffee is a great honor. If you find yourself invited to an Ethiopian coffee ceremony, remember to stay for all three servings. After the coffee is roasted, ground and brewed (a series of sacred tasks done only by women) the coffee is served in three rounds, abol, tona and baraka. You are right to think baraka and Barack might be related. The last round of the coffee ceremony, baraka, just like the name Barack as in Barack Obama, means blessed. Baraka and Barack both come from the semitic language group which includes Hebrew, Arabic and Amharic (the language of Ethiopia).
Nowhere could I find a satisfactory etymology for the other two rounds of coffee, abol and tona. Some claim that they simply mean first round and second round, respectively. I imagine there is a better story than that. If you know where these words come from let me know!