Renewal of Passport before FLR question

[PearceLefey]

Hello there! I am new to posting to this forum but have referenced topics from here to help me on sending out my Settlement-Fiance Visa. The visa is still processing but whileso, I had some lingering questions that I cant seem to find an answer to.

My question and a bit of my situation is this; My projected move is end of June, and my wedding will be end of August. After getting married I know Ill have to change my name on my BioPermit, Passport, and Social Security. But, my passport expires April of 2020, and I was wondering what steps I should take before applying for my FLR Spousal.

Do I have to send out for a passport renewal with my marriage certificate as proof to renew and change my name, then my social, then apply for the FLR? Or will I be cutting it close on my 6 month fiance visa ending eventhough I got married before the 6 months? Me and my fiance wanted to go apply for the Spousal FLR in person to get it done faster, but waiting for my passport to be renewed and changed [not sure what happens to my visa] and then waiting for an appointment may push me over my visa time.
I am at a loss for what steps I should take.
Thank you to whomever can clarify!