Most adoptive parents have been thinking about it for a long time and might have names picked out before they even know the ethnicity of the child they'll get to adopt. Also, you seem to be confusing "white" (which generally means Caucasian) with ethnicity. Most who bear the Spanish name Jose' would be "white" as in would be Caucasians of Spanish or Latin American ethnicities.
In my experience, if a white couple adopt a child of another ethnicity or nationality, they are somewhat more likely than not to give the child a name that reflects his or her ethnicity. You'll see this most often with Asian adoptees. It doesn't happen with white parents and black adoptive children (most black Americans have ordinary names, despite the claim among racists that they're all called "Laquan" or something), but I'd imagine it's not uncommon with white parents and Hispanic adoptive children.
We don't really see many Hispanic parents adopting Anglo children, or many black parents adopting white children, so there probably aren't enough examples to say what's "normal".
Answers & Comments
Most adoptive parents have been thinking about it for a long time and might have names picked out before they even know the ethnicity of the child they'll get to adopt. Also, you seem to be confusing "white" (which generally means Caucasian) with ethnicity. Most who bear the Spanish name Jose' would be "white" as in would be Caucasians of Spanish or Latin American ethnicities.
It's not uncommon, especially if the adoptive parents can't pronounce the baby's original name
No, but parents can do as they please.
In my experience, if a white couple adopt a child of another ethnicity or nationality, they are somewhat more likely than not to give the child a name that reflects his or her ethnicity. You'll see this most often with Asian adoptees. It doesn't happen with white parents and black adoptive children (most black Americans have ordinary names, despite the claim among racists that they're all called "Laquan" or something), but I'd imagine it's not uncommon with white parents and Hispanic adoptive children.
We don't really see many Hispanic parents adopting Anglo children, or many black parents adopting white children, so there probably aren't enough examples to say what's "normal".