Rank name based on a score, but input the names as the ranked value?

I have a list of names, all with a certain score attributed to them. I would like to, on a separate worksheet, rank these names by their score but have the formula input their name instead of 1st, 2nd, 3rd, etc. Now it sounds simple, but the position these names are ranked will be changing constantly, and I need the formula to automatically reposition them properly in the rank, while keeping the same name showing.

I've read a couple threads somewhat like this, but none of them really answered my question. Also, I've read a few threads where providing a sample workbook was requested. I have no idea how to do this. If it would help, let me know how to do it or point me in the right direction to find out how to do it.

Thanks!

(I had problems uploading a workbook too.)
But where are your names? Will they all be in column A? Or some other column?
Where are the scores? Will they be in column B? Or some other column?
Will they start at row 1 or row 2 or some other row?
The names & scores are on which worksheet? "Sheet1" or some other name?
The names & scores ranked are to be on which worksheet? "Sheet2" or some other name?

The names are all in column A, from A2 to A38. The scores are in column H, from H2 to H38. These are both on worksheet 1, named "Sheet1". They are to be ranked on worksheet 2, named "Sheet2". I would like each name in the A column to be ranked by their score in the H column, but not be displayed as "1, 2, 3, etc." in Sheet2. I would like them to be displayed as their name. Is this possible?