HOW TO SOLVE INDEX MATCH WITH DATE TENURE?

This is Table 1

This is Table 2

The criteria is Match the Date & Name from Table 1 to find the Amount and put it in Table 2. And also add the amounts which is under the date tenure for the specific month.

After many research I have found a formula which can mach 2 criteria at once but its not working for add the amounts for specific date tenure.

{=IFNA(INDEX($C$2:$C$8,MATCH(1,(($A$2:$A$8=$E2)*($B$2:$B$8>DATE(2020,1,31))*($B$2:$B$8<DATE(2020,3,1))),0)),0)}

Please help me to add the amounts which will have in the date tenure.