Here's what I THINK the process is (at least for my situation- FLR(M) and changing my name):
Get a visa (sticker in passport) in maiden name passport
Get BRP (card) in maiden name
Get passport in married name
Get BRP in married name (not sure if we have to pay or how much or exactly how to do it, but it sounds like you have to notify them whenever you officially change your name)
Two options next:
1. Carry maiden passport (with visa), married passport and marriage certificate when travelling
2. Get visa transferred from maiden passport to married passport (£220 by post or £661 in person)
The visa sticker always matches the passport it's in. So if it's in your maiden passport, it will be in your maiden name. You can choose to have it transferred, but carrying proof it's you (see option 1) is good enough.

When it comes time to apply for ILR, it will go in my married passport. I will have to submit my maiden passport as that will have my FLR(M) in it.
Do I have that right?