The following version will first create sheets, then save those as separate files and delete the sheets.

ExcelMultipleWorksheet

Sub SplitData()
    Const NameCol = "Change this to Column ID A or B or C..."
    Const HeaderRow = 1
    Const FirstRow = 2
    Dim SrcSheet As Worksheet
    Dim TrgSheet As Worksheet
    Dim SrcRow As Long
    Dim LastRow As Long
    Dim TrgRow As Long
    Dim Student As String
    Application.ScreenUpdating = False
    Set SrcSheet = ActiveSheet
    LastRow = SrcSheet.Cells(SrcSheet.Rows.Count, NameCol).End(xlUp).Row
    For SrcRow = FirstRow To LastRow
        Student = SrcSheet.Cells(SrcRow, NameCol).Value
        Set TrgSheet = Nothing
        On Error Resume Next
        Set TrgSheet = Worksheets(Student)
        On Error GoTo 0
        If TrgSheet Is Nothing Then
            Set TrgSheet = Worksheets.Add(After:=Worksheets(Worksheets.Count))
            TrgSheet.Name = Student
            SrcSheet.Rows(HeaderRow).Copy Destination:=TrgSheet.Rows(HeaderRow)
        End If
        TrgRow = TrgSheet.Cells(TrgSheet.Rows.Count, NameCol).End(xlUp).Row + 1
        SrcSheet.Rows(SrcRow).Copy Destination:=TrgSheet.Rows(TrgRow)
    Next SrcRow
    Application.ScreenUpdating = True
End Sub