I have a table like this:
Row Name Y/N? No. of Y
1 Adam Y 1
2 Adam Y 2
3 Adam N 2
4 Adam N 2
1 Brian Y 1
2 Brian N 1
3 Brian N 1
4 Brian Y 2

Is there a formula I can put for "No. of Y" that counts the no. of times "Y"
appears for Adam from the first "Adam" row up to the current row? The
counting should restart for Brian and not accumulate from Adam's total.

Note that the starting point for each person is when "Row" = 1.

Can a pivot table help?