The branding of yore was in part created by the industrial production needs; a CD is a stable item, a product you want to go through certain standards before putting it out through the door.
The name of the band doubled then as the product brand; "the name you know". The simple word, the logo, evoked a series of emotions, the consumer knew very quickly what to expect to find in the package. The examples are many.
But the coin in music always has too sides, so the product is also a piece of art. This brand thing often turns out to be, even now, a nasty restraint for artists, human beings who advance in their life journey, make mistakes, mature, learn, and sometimes want or need to give musical expression to those experiences; or simple try something new for the heck of it. Neil Young comes to mind, with his electronic experiments, or his concerts where he refused to play "the hits", a commercial suicide I guess, even though he provided fair warning.
A more recent example is a member of Testament saying that they have a certain fear of going too far with experiments and cause deception among fans. There are also examples of bands who seem to change just because, whimsically, without a clear purpose (Megadeth is in my view the big representative).
As for my own case, the baseline I'm using in this matter, and this is an eternal work in process, is considering branding as an act of "politeness" towards the audience.
I create freely, I don't reject anything that comes knocking to my brain, but then I draw those "lines in the sand" not to confuse listeners, who are often highly especialized.
Like I say, these are lines in the sand for me; so I'm not too clingy to the "brand"; to me it is a provisional thing, useful but somewhat arbitrary. Also, it is not so meaningful nowadays, with the CD gone and the production means changing, and the listener preferences moving and hopefuly evolving.
In the end, the hour of truth is the live event, and there brands take a back step in relation to the human experience; you just do what works for the hour. The act can be publiziced as "Ozzy Osbourne" but nobody will protest if he sings a Sabbath song. Or, back to Neil Young, he often plays songs that, in purity, belong to the "Crosby Stills Nash & Young" band. Will someone go "Hey, I want my money back!" when the first notes of "Ohio" start to sound? I highly doubt it.