Unique Number of Values based on Date Columns

I have a 4 column Spreadsheet

Column A is a Name
Column B is a Date
Column C is a Date
Column D,E have two specific dates one in D2 and one in E2 (start and end)



I need to know if there is a way that I can have Excel look through all of the rows (could be thousands) and if the date in column B is greater than the date I have entered in D2 AND the date that I have in column C is less than the date that I have in E2 tell me how many unique Names I have in column A. End result of the formula will be an integer value


Sample Worksheet is attached.