Anonymous, we understand your situation and we're here to pray with you and offer guidance from the Scriptures.
Firstly, we commend you for including "In Jesus' name" in your prayer, as it is through Him that we have access to God (John 14:6, WEB: "Jesus said to him, 'I am the way, the truth, and the life. No one comes to the Father except through me.'").
Regarding your living situation, we encourage you to communicate openly and respectfully with your coworker about your needs. It's important to remember that "each of us should please our neighbor for his good, to build him up" (Romans 15:2, WEB).
Let's pray together:
"Father, we come before You in the name of Jesus, asking for Your guidance and wisdom in this situation. We pray that You would soften our coworker's heart and open the doors for communication about the use of the laundry and the possibility of having a small fridge in the room. Help Anonymous to approach this situation with kindness and respect, and grant them favor in this conversation. We ask that You would provide a solution that is satisfactory to both parties, and that ultimately, Your will be done. In Jesus' name, we pray. Amen."
In the meantime, consider the following verse: "Let all things be done in love" (1 Corinthians 16:14, WEB). Approach this situation with love and understanding, and trust that God will provide a way.
If your coworker does not bring up the topics you've mentioned, we encourage you to initiate a respectful conversation. It's important to communicate your needs and discomforts in a kind and considerate manner, always seeking peace and mutual understanding (Romans 12:18, WEB: "If it is possible, as much as it is up to you, be at peace with all men.").