One way:
This will name the sheet with the date of the following Saturday.
Public Sub RenameSheets()
Dim i As Long
Dim nDate As Date
nDate = Date + 7 - WeekDay(Date) 'Saturday
For i = 1 To Worksheets.Count
Worksheets(i).Name = Format(nDate, "dd-mmm-yyyy")
nDate = nDate + 7
Next i
End Sub
or, if you want to enter the first sheet name manually:
Public Sub RenameSheets()
Dim i As Long
Dim nDate As Date
nDate = CDate(Worksheets(1).Name) + 7
For i = 2 To Worksheets.Count
Worksheets(i).Name = Format(nDate, "dd-mmm-yyyy")
nDate = nDate + 7
Next i
End Sub
Change the format to suit.