Hi,
What I understood you want max repeating month and year for particular name. If so, see the attached file. Below formula is used.
1. Things to note (Use of Aggregate function so will be working in Excel 2010 & above).
2. Array function so must be enter be Ctrl+Shift+Enter.
Formula in I2. Copy till M4.
=IFERROR(INDEX($C$2:$C$38,AGGREGATE(15,6,IF(FREQUENCY(IF($G2=$B$2:$B$38,(MONTH($C$2:$C$38)&YEAR($C$2:$C$38))+0),IF($G2=$B$2:$B$38,(MONTH($C$2:$C$38)&YEAR($C$2:$C$38))+0))=MAX(FREQUENCY(IF($G2=$B$2:$B$38,(MONTH($C$2:$C$38)&YEAR($C$2:$C$38))+0),IF($G2=$B$2:$B$38,(MONTH($C$2:$C$38)&YEAR($C$2:$C$38))+0))),ROW(OFFSET($C$2,MATCH($G2,$B$2:$B$38,0)-2,0,COUNTIF($B$2:$B$38,$G2)))),COLUMNS($I2:I2))),"")
Just advise if you need any other thing.
Regards,