It is mentioned in the “Al Muwahib Al Ludaniyah” of Al Qastalani and his explanation to Al Zarqani, that the battle was named the battle of those with patches because they had patched their banners, or was based on the name of a tree in the area that the Arabs used to worship and they would tie pieces of cloth to it so that their wishes would be fulfilled.
It is said: because the land that they had descended on had black and white patches like a patched shirt. It was also said that some of their horses were black and some were white.
The most correct saying is the narration of Bukhari and Muslim that the lack of camels forced some of the Muslims to walk, which was tough on their feet, so they would bind their feet with pieces of cloth to help reduce the pain of walking on the uneven land.