I agree, there is no problem, as YOU are the claimant, not your partner.

I claimed child benefit for my two stepchildren (a long time ago), but essentially the rules were the same then.

They need to know about your partner and the children, with proof, because people DO make up fraudulent claims of course. They just want to be sure that they do exist !

These benefits can be claimed by and paid to either partner. That's perfectly normal.