Logic to group rows as one batch based on created date and Rank

I cannot match your expected data as weeknum is giving the same for your rows 2 and above.

I created similar dataset and able to get these results 

Using Dax Columns:

Rank Column = RANKX ( 'Table', WEEKNUM('Table'[Date]),,ASC, Dense)

Batch Name Column = "Batch " & [Rank Column]

Current Batch Column = If ( [Rank Column] = MAX (  'Table'[Rank Column]  ) , "Yes", "No")

I think it will be good to have measures for this scenario, so providing the syntax for that also:

Rank Measure = RANKX( allselected('Table'), WEEKNUM(  CALCULATE( max('Table'[Date]))) ,,asc, dense)

Batch Name Measure = "Batch " & [Rank Measure]



Current Batch Measure = 
var _Max = MAXX ( all('Table'),  [Rank Measure] )
RETURN If ( [Rank Measure] = _Max , "Yes", "No")

If the source data and your expectation is per your post, then adjust to your needs the weeknum portion of DAX. 

Hope it helps!