It sounds like the VLOOKUP() function will do what you want.
VLOOKUP() takes a series of parameters (look at the help file for details).
The first parameter is the value to be searched for - which will be the value in the drop-down cell.
The second parameter is the range which contains the name being searched for in the first column and the percentage in the second column, so a range like Sheet1!$A$1:$B$20, then the column number of the result in that range, 2 in this case if percentages are in column B. The final parameter will be FALSE (not in quotes), which ensures that a result is only returned for an exact match of the data.
Here's one I made earlier: