Board Thread:Questions and Answers/@comment-34660304-20160530142632/@comment-27542229-20160530202343

Left shield is a character's allegiance by birth. The right shield is a character's current allegiance, which, for women usually means the house they married into. For Brienne, she is now the sworn shield to Sansa Stark so the House Stark shield should be on the right (which I have just edited).

For men, the shield on the right typically does not change though Tyrion Lannister is a good example of a character switching allegiance.

One minor rule - the right shield is also the space to show a character's personal sigil such as the Blackfish.

The middle shields are for past allegiances. For Brienne, she gets one for Renly Baratheon. Jon Snow has a Night's Watch shield in the middle now to denote his past allegiance to Watch.

The middle shields are generally not used that much.

Brienne is an unusual case in that she is a sworn shield of two particular women while most other characters are sworn to a house and serve the lord of the house.

I hope this helps - let me know if you have any further questions.