Wife passport name changed

My wife's name changed on her new passport (due to marriage) and her residence card is registered with her old passport.

We got her new passport quite some time ago (5 months ago) and we have not yet reported to immigration office.

We plan to go on this Thursday and just saw from their official site that report should be made within 14 days from the date of the change...

Will there be any problem when we get there?

Somehow from your post, I assume your non-Japanese wife is here on gspouse of Japanese nationalh or some other family relationship-based status?

They can make a hassle saying how could you forget such an important report (the name change is one thing, and the passport number – I guess it changed too – is another. She would need to have the landing permission/resident status transferred from the old passport to the new one, wouldnft she?), to which all you can is just apologize profusely to them for the late report, that you did not know that the report had to be made within 14 days, and that you will be prompt with reporting in the future (be sincere in saying these things). There should be no consequences in the sense of penalty or anything. Best wishes.

(Written by the Japanese wife of a non-Japanese national living in Japan)

immigration is the first place to report the change.
you may need to take necessary paperwork to change the name of "my number" card, resident registration (at city office), bank accounts, health insurance, pension, credit cards, etc.

if you get married, the calculations of many things, like income tax, health insurance, pension, etc. may be changed, depending on your situation. when you report your marriage, they will re-calculate the fees.
reporting your marriage is definitely more beneficial for you than no actions.
do them with no delay.