State Pension payments are normally made every four weeks in arrears but they can be paid weekly in advance.
The pay day is based on the final on the final two digits of your National Insurance (NI) Number. Monday is the pay day for numbers 00-19 and so on until 80-99 which have a Friday pay day.
The pay days are allocated automatically by the payment systems and although legislation allows the Secretary of State to allocate a different day, in the many years I worked for DWP, I never came across someone where that happened.
Having been allocated a pay day, I'm not aware it's even possible to change it now.