I suppose that it isn't really the same name with two different roots. That would be strange.
Sabrina the river got its name long before any English-speakers had ever encountered a prickly pear - in fact, long before there were English people in Britain. My guess would be that if someone named a child
Sabrina rather than Sabra but wanted the Israeli reference, then they'd pretty certainly be Jewish themselves. And a child named
Sabrina who wasn't in any way connected to
Israel would identify with the river, or the character in
Milton's Comus.
I've never met anyone named Sabra, though there used to be a brand of tights (which laddered as quickly as any others) and a chocolate-orange liqueur (very nice) with the name. Both made in
Israel.