How to count frequency of occurrences in the last 7 days when data has date/time

Here is the sample dataset, having 2 columns, Data, and Name

The problem is to create a measure that is going to count the number of name occurrences having a count greater than 2

Step 1 is to find the Names that show up at least once a day without a timestamp

Step 2 is to find names that have occurrences of more than 2 from the output got of Step 1:

Step 3: is to get the distinct count of names from Step 2:

Expected Output = 2

Not sure how to do this in DAX.

Note: I m looking for a measure that gives the Output = 2 and not the steps, the steps are for understanding purposes/ or to provide clarity

First write a measure to count the names

Measure = CALCULATE(COUNT(Data[Name]), FILTER(ALLEXCEPT(data, Data[Name]), Data[Date] <= DATEVALUE("2023-05-07")))

Then use that measure to count names more than 2

Measure 2 = CALCULATE(DISTINCTCOUNT(Data[Name]), FILTER(data, [Measure] > 2))

If you either split your date and time column into separate columns or create them in your fact table, then this is trivial using FILTER and COUNTROWS() and maybe RELATEDTABLE().

Testing for updated list:

I basically did this:

Measure = 
var base = 
SUMMARIZE(data,Data[Name],"Count",count(Data[Date]))
return calculate( countrows(filter(base,[Count] >2)))

which gives the output: Sam(8), Tim(3), Ahmed(3), Jake(4), Oscar(3)

Then to get the count of frequent names in the last 7 days I use the below measure:

Measure 2 = 
var last_7 = now() - 7
return calculate( [Measure], filter(Data, Data[Date] >= last_7))

The result is shown below: Checks for count more than 2 times in the last 7 days (that is starting 5/5/2023), The result is 2, because the counts>2 are Sam(5) and Oscar(3).