MY brother as given me his old iphone. Do I need to register that I am new owner with Apple?
It would be a convenience if you needed Apple support, but it isn't required.
Hopefully your brother did the steps shown here:
What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support
Like Lawrence said, it's not completely required. It would be a good idea for you to register it though just in the case you need to use Apple Support.