Creating a form - choosing only selected dates

Good day,

I created a tracking sheet (Date, assigned to, and Safety share Title). After I created the sheet, I want to create a form that users can complete. In this form users should only be allowed to pick selected dates in correspondence with their name. For example: Feb 3, 2020 safety share is assigned to Tom, he needs to be able to select the date that is correspondent with his name and fill in his safety share title. As you can see the dates is every Monday. Is this possible?