Upvote:1
As a rule, no, it's not a problem, assuming nothing else has changed (meaning you booked your ticket with the new name, and do not need to change this as well). You can give them the new passport number when you check in.
Upvote:2
If your personal details (such as name, date of birth, etc.) will remain the same, then you can provide your new passport at the checkin desk without issue.
The API (Advanced Passenger Information) that includes among other things your passport information can be updated as long as the flight has not departed.
If your old passport contains a valid visa, then you must carry it with you along with your new passport and present both to immigration (if required, for your destination).