Is tearing up a paper on which the name "Muhammad" is written and throwing it in the trash considered disbelief (kufr), especially with the presence of satanic whisperings (waswasah)?

What you have done does not amount to disbelief (Kufr), and you must treat yourself for obsessive thoughts by completely ignoring them. The names of prophets, when used for others, do not carry the same sanctity, and it is not obligatory to revere them, unlike when they are accompanied by phrases indicating they refer to a prophet, such as: "Muhammad is the Messenger of Allah" or "Jesus, peace be upon him."