You must tell your mortgage company, but it is doubtful they will raise the rate.
This is because if they ever need to repossess, they will be aware of the non-family member resident in your house and the terms - they will not want a sitting tenant they can't evict.
You must also tell your insurance company - your insurance may go up, both buildings and contents.
If you currently get a single occupants' council tax discount, you must inform the council tax office as well.
You should be able to write your own agreement - include the rent, when and how it should be paid, and specifics such as telephone call costs.