Change of passport name after marriage?

[Terpe]

Did anybody change their passport name to their spouse's surname after marriage in the UK and before applying for their FLR(M)?.....

Some folks have ...but most don't.
As melovesengland says, timing is key. There's absolutely no pressing reason to change the name in the passport. Better to minimise risks by waiting a while and focus on getting married and submitting the application for FLR(M).
It really doesn't prevent your wife from using her married name in all her day-day affairs such as bills, banking etc.

Most folks don't renew passports until they need to.

.My concern is that the new passport would not contain the current (fiancée) visa when applying for the FLR(M).

Doesn't make any difference.

Form FLR(M) asks for details of both current passport and previous passports.
Also for the name on the current passport and for other names that you have been known by.
Home office records will link with this or with any previous HO reference number.

I'd suggest keeping things as simple and risk free as possible