In the "Ogden's Sign" quest, a creature has stolen the sign from the tavern because it has the image of a sun on it, and some other creatures have in turn stolen it from him. The creature calls it a "magic banner" instead of a magic sign, because he intends to use it as a war standard. If you give the sign to the creature he says:
"You give! Yes, good! go now, we strong! We kill all with big magic! (laughs)" From Diablo Wiki
The image of the tavern sign shows it as hanging from a pole, so it could be carried like a standard, or "a conspicuous object (as a banner) formerly carried at the top of a pole and used to mark a rallying point especially in battle or to serve as an emblem." Something like this:
A banner in this sense is not interchangeable with sign, because it is more symbolic than a simple sign. "They marched under the White Queen's sign." wouldn't make people picture the same thing as "They marched under the White Queen's banner." A banner (in this context) is a symbol of something that people might rally around. A sign (in the sense of a tavern sign) is just an informational display.
A related idiom is "under the banner of" something, which Collins dictionary explains as
If someone does something under the banner of a particular cause, idea, or belief, they do it saying that they support that cause, idea, or belief.
For example (from Collins dictionary),
Russia was the first country to forge a new economic system under the banner of Marxism.
Another related idiom is "standard bearer", which Collins dictionary describes as
If you describe someone as the standard bearer of a group, you mean that they act as the leader or public representative of a group of people who have the same aims or interests.
For example,
The opposition has also been wracked by infighting since the February death of longtime standard bearer Etienne Tshisekedi.
(Source: Reuters )