Facebook help please - changing names/search engines?

If you鈥檝e enabled search engines like Google to find your name and Facebook link when searching for your name, but then you change your name IN Facebook under settings how do you make it so when you search in Google for your new name your FB link comes up?



Ex. My name is Betty Sam Smith. My Facebook name was Betty S Smith:

First name: Betty

Last name: S Smith

And I changed it to Betty Smith.

First name: Betty

Last name: Smith



I tried to re-set the Search page under Privacy in Settings and I waited the 24 hours and it never changed, it still comes up as Betty S Smith.
Facebook help please - changing names/search engines?
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