can i fly using my old passport whilst waiting for a name change to be processed?

extra context, i’m from australia.

i need some advice!! i’m planning an emergency trip to california in december, the only problem is that i’m stalling to buy tickets because i am waiting for my name change to process.

i have changed my last name for personal reasons. i put in the application two weeks ago and it apparently will still take three more weeks for it to be approved and processed. i do not want to hold on booking my flights any longer as they are soaring in price and i am a little strapped for money.

my question is- theoretically, can i book the flights and fly with my ‘old’ passport that has my old last name on it? i haven’t ordered a new passport, so my sole passport is the one with my old last name. as long as i book the ticket with the last name matching my passport i should be okay, right? i have no idea when my name change will be accepted and haven’t put in an application for a new passport as it is very pricey.

should i risk it or just hold off until my name change has been approved?