What should we do with papers that contain the names of prophets or the Basmala and are thrown on the ground, and is tearing them into small pieces so that no complete, meaningful name remains a correct way to dispose of them?

Papers containing anything that is glorified in Islamic law, such as the Basmalah, or the names of Allah or His prophets, must be preserved in a suitable place or burned. The origin of burning is what Uthman (may Allah be pleased with him) did when he ordered the burning of every Mushaf or scripture that differed from the Mushaf he had compiled, because in doing so there is honor for them and preservation from their desecration. Tearing here is like burning, because the intent is to prevent these papers from being exposed to desecration.