Am I obliged to do anything if a bag with the name "Mecca Al-Mukarramah" written on it is used as a trash bag, after I had hung it up with the intention of burning it out of reverence for the name of Mecca?

The name "Mecca" and any name revered in Islamic law should be protected from disrespect, such as discarding them in the trash. This is because Mecca is the cradle of revelation, and Allah Almighty mentioned it in the Quran and swore by it. It is also the most beloved city to the Prophet, peace be upon him. It is disliked to dishonor its name or to throw papers bearing its name into the trash. However, this does not reach the level of prohibition unless one deliberately intends to disrespect it. Users of papers must inspect them before discarding them, and there is no sin upon someone who forgets or does not pay attention.