Hey everyone I live in the UK and my partner wants to put my name on his rent book

We are both on benefits, I work although only 12 hours a week for a little extra

He has bad mental health and a list of problems wrong with him and is on pip and esa plus he gets all off his rent payed for him

I'm on child benefit,carers allowance & income support

Will him putting my name on the rent book affect any off our money ect?

We also have a 2month old daughter

Many thanks!