For a flight to the Philippines, is it a problem if I submit my old passport number when I booked the ticket? I applied to renew my passport, in order to make a name change. I have to book a ticket now, but my new passport has not yet been received. How should I handle this?
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).
As a rule, no, it's not a problem, assuming nothing else has changed. You can give them the new passport number when you check in.