Lola,
Be careful in doing that though. If you make a travel reservation under your new name and your passport hasn't been amended the airline may prevent you from travelling. To avoid this, be sure that all travel reservations are made in your old name until your passport get's updated.
My wife and I planned a dive trip to Palau for 16 months, and almost didn't get to go b/c of that passport issue, we eventually were allowed to depart after my wife went home and got our marriage license from the safety deposit box.
Stephan