My surname is not written in my passport in Surname column

My surname is not written in my passport in Surname column.
It is written in as Given name.
Given Name - my name and surname.
I am recently married and my wife could not take my surname because it is not mentioned in my Passport.

If I will renew my passport, I will write my surname in surname, name in given column. and my wife’s current name without my surname.
that means I will renew my passport two times.

Only after renewing my passport my wife can take my surname.
that means once when she takes my surname then I have to renew my passport again?

it means I have to renew two times my passport?
Please help. Many thanks in advance.

I don’t understand as to why you need passport renewal twice?