Since Rank is a table function, you'll have to hide the items you do not want to be displayed but still considered in the Rank. If you have groups that segment the names you could hide all the groups and show the one you are interested in. The rank will remain the same. When you filter, rank will update based on what is in the table.
Hope this Helps!
You can change your filter to a 'late' table calculation filter. Create a calculated field along the lines of LOOKUP([Collector Name],0) and use that as your filter.
What Andrew said ^^
Regular filters physically exclude rows from the table that Tableau is using for the sheet. With rows excluded, table-wide operations get changed. (Ranks. Running sums. Percent-of-total, etc.)
Table calc filters exclude what gets shown on the sheet, but do not exclude physical rows from the underlying table, and therefore table-wide operations remain intact.
LOOKUP() is a great way to make such a table calc to use as a filter.