Spouse visa surname issue

Will I have issues getting a visa in Japan if the surname on my Certificate of Eligibility is under my maiden name while my passport is under my married name (Japanese surname)?

you mean that you got married with someone during your application of COE (for example, for working) and the COE was issued with your old name, but you have a passport of your new name (after married) at present.
ask the Japanese embassy in your country. but, in general, you can prove your name change by a set of your new passport, your old passport, and the certificate of the marriage.

I got married first last Sept then He passed the Marriage certificate in Japan last Nov and applied for COE in japan last Dec. but I got my new passport with the new surname last Nov as well. I already passed my old passport and marriage certificate PSA and Local Civil Register at the agency where I applied for a visa. He called the Immigration in Japan saying that that it would be alright as long as we have provided the necessary documto prove that it is the same person however i emailed the embassy here in the Philippines but they stated that i have to get a new COE with the new surname. That's why it's very confusing.

he applied the COE in Dec. 2023 with your old passport (so that, the COE was issued under the old name), but, you already had a new passport (with new name) in Nov. 2023. so the application of COE was incorrect (applied with an invalid passport).

if my understanding is correct, he (a Japanese) asks the name change of the COE in immigration office with an apology of application mistake.

Yes, there was a mistake upon submission of the COE. application. Is this possible? Have someone done this before?
One more thing, I already passed and applied for a spouse visa last April 4. Will it be denied or will the embassy require us to apply or change the surname on the COE?