Formula to Sequence Based on Date and Name

I have a list of Names in cell A and Dates (Date & Time) in cell B. Each row is a message interaction. I want to create a formula that will sequence message order for me(column C below).

See Example Below:

Column A Column B Column C
Alan 9/15/18, 1:08 PM 3
Alan 9/15/18, 1:02 PM 2
Brad 9/13/18, 1:02 PM 1
Alan 9/13/18, 1:30 PM 1
Brad 9/14/18, 1:02 PM 2
Brad 9/15/18, 1:02 PM 3

assuming the above data set was housed in A2:B7 (i.e. row 1 is header)

Formula:

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the range references can be made to dynamically adjust, if required (i.e. dataset is large)

Personally, I would always advise against using COUNTIFS with entire column ranges (A:A etc) in large volume -- whilst COUNTIFS is less intensive than an Array / SUMPRODUCT equivalent it can still be quite resource intensive if used extensively.