To make life a bit easier in C1 enter
=20-COUNTIF($B$1:$B$19,"<"&B1)-COUNTIF(B1:$B$19,B1)
and copy down to C19, this will give you a rank of scores High to Low. Where there is a duplicate score the first in the list is ranked higher than the second, but all will be included.
Then in A21 you can enter a formula that references this list, enter
=INDIRECT("A"&MATCH(ROW()-20,$C$1:$C$19,0))
Which will form a reference to the name in column "A" against the row number for the highest score which it finds in "C" copy this down to A39. And in B21 enter
=INDIRECT("B"&MATCH(ROW()-20,$C$1:$C$19,0))
Which will match the scores to the names.
These formulas are specific to the data you gave as an example so if there are more than 19 students it will have to be adapted. But that is just a matter of changing a few numbers. And you can always hide column "C" if you don't want to see it on your sheet.
Just as a note in the first formula change "<" to ">" to sort the list low to high
Regards
Steve