Minecraft wiki entry for Banner, associated text: With 16 blank banners, 38 patterns of 16 colors each (608 uniquely-colored patterns), and 0 to 6 patterns per banner, the number of uniquely crafted banners is 16 × (6080 + 6081 + 6082 + 6083 + 6084 + 6085 + 6086) ≈ 809 quadrillion (809,573,616,779,945,488). The number of visually distinct banners is smaller, because one or more patterns may completely cover other patterns, or the entire banner, or be duplicated due to the symmetric set of patterns (e.g. field or (yellow) + per pale azure (blue) = field azure + per pale or inverted).
If a banner has over 6 patterns, only the six bottom-most patterns are displayed when hovered over in the inventory.
The Mojang Logo is called "Thing" in-game, which could be considered an alternate translation for mojäng. If Google Translate is used, it translates to "thingys" or "contraption".
In the Swedish translation of the game, this pattern is, in fact, called mojäng.
Banner textures are located in \assets\minecraft\textures\entity\banner.
There are 40 monochrome textures, each containing all 6 sides of the banner.
The texture of the back side is the mirrored texture of the front side.
Compared to the texture files, textures' colors are inverted in-game due to them acting as masks for the re-colored base texture, base.png. That means white is visible, while black is transparent.
Banners that have the purple NBT+ line in the bottom (obtained by holding Ctrl and middle-clicking the banner, which also copies the NBT tag of anything that the player points their crosshair to) actually have no difference with the base banner obtained by middle click.
The Illager Banner in Bedrock Edition is available as a separate item but is just a second variant of the white banner.
Standard variant of white banner is set to type 0.
Illager variant is set to type 1.