You have to send letters and copies of your Name Change After Marriage certificate to EVERY business and agency that knows yu by your maiden name. Like your bank, your driving licence, doctor's, etc. As for your passport, depends what name you have put on the travel documents. If you have used your maiden name, then keep the passport as your maiden name until you get back from travels. The last thing you want is to stress whether or not your amended passport is going to be returned to you in time for your wedding!!!
Of course you can call yourself "Mrs" on the day. I did, and I haven't changed my name!