Follow this sequence:
Assuming names are in column A and scores in column B, with headings in row 1.
1. Create a list of the unique names.
Select the column containing the names, select 'Filter' - 'Advanced Filter...'
In the Advanced filter dialog box select 'Unique records only' and 'Copy to another location'. Enter a single cell Address in the 'Copy to' box - I used D1
2. Find the highest score for each name
In the column next to the unique names, starting at E2 (row 1 contains column headings)
enter this formula:
Change the end of range $A$1001 and $B$1001 to match the end of your list of names)
Select cell C2 Select cell E2 and drag the formula to extend it down alongside the list of unique names.
You now have the highest score alongside each individual
3. Rank the individuals
In E2 enter this formula:
Change the end of range $E$8 to match the end of the range containing the unique names.
Drag this formula down to extend it alongside the list of unique names
This will give you the rank values