I am just over the age of 22 and taking a 1 week trip to Japan.

I have different surnames on my Australian and Japanese passports like so:

Mary Jane Smith

Mary(Jane) Suzuki(Smith)

and I have bought my plane tickets under my Australian name (Mary Smith).

What would you advise is the best way for me to enter and leave Japan, as being a dual national is technically illegal? I have heard to show both passports at the airline's check-in counter and then the passport for the country I'm in at immigration/customs but I'm not sure if this advice still applies if my surname is different. Does the immigration counter in Japan need to take a look at my plane ticket?

Thanks!