There's really no pressure to renew your passport. Name changes on a passport are really of no importance at all.
My personal suggestion to you, is to get that FLR done and dusted as soon as you are married. That is the key priority.
You may still use your new married surname if you wish anytime you want. Your marriage certificate is the link.
BTW may I suggest getting 4 or 5 marriage certificate copies at the time of your marriage. They will come in very handy.
Another nice idea to think about is to consider having your maiden name as your new middle name. This follows Philippine tradition and also keeps a nice track for all subsequent documentation. Quite a large number of people will do that, but it's up to you.