Passport and name change issue?

Hi all!

I’m getting married in May and I’m taking my husband‘s last name. We have our honeymoon date set for a month after the wedding. We are worried about submitting the marriage certificate and changing my last name before and having issues with the passport since we are traveling to Europe from the USA. I thought I saw that you could submit it up to 60 days after the wedding. Is that right? I also saw that you could later on submit a name change application but they cost around $400. Has anyone dealt with us or have any advice?

Thanks!