Hi,
It's not possible to have dynamic prompts, they are set on a report and a user must choose from the prompt options available to filter the results to their needs every time they view the report.
However, have you considered using wildcard filter variables instead? From what you have described this should meet your needs. For example, of you were to add a filter rule of homeTeamID equals $$USER.homeTeamID, the report would dynamically filter to the team of the person viewing that report.
You can read more on wildcard filter variables here
Best Regards,
Rich.