The cosmetic surname doesn't much matter.
But, he should not appear as the registered father
when he knows that to not be the truth.
This is because there is an obligation to provide BDM with
information that is "true and correct".
It's important to update BDM records
when what you know to be true now
turns out to be different to what you "knew" then.
He basically has no obligations to pay Child Support to a child that is not his
(There are some ifs and buts of facts and circumstance attached to this statement,
but I don't know enough to know if they apply here, and I'm trying to keep it brief and clear).
Even if he chooses to pay something voluntarily, he should not hand over money directly to the child's mother.
Also, any voluntary payment he makes will not in itself generate a right to see the child.
He has no prima facie rights to be involved in the child's life.
The child, however, may have some rights to a relationship with the key people
in their life (including the social "father figure").
Make no mistake - your brother will find this all very, very difficult.
He will be going through a very complex and intense set of emotions,
which will call on every part of his maturity, strength, and resilience.
He will, for example, find it very difficult indeed to summon the wherewithal
to remove the mother from his life, immediately and completely.