you don't need to pass the parameters at all, because the"Target" has all the information needed so I reckon it can come doen to something like this ( note not tested)

Private Sub Worksheet_Change(ByVal Target As Range)
     
   
        If Not Intersect(Target, Range("B9:C43")) Is Nothing Then
            Call StudentAssign(Target) 'Student i
        End If
      
End Sub


Private Function StudentAssign(ByRef Target As Range)
     'Student Auto Assign sheet name and student name on report card - check list - Grading sheets
     
    Dim intws1 As Integer
    Dim intsw2 As Integer
    Dim intBcell As Integer
    Dim strCcell As String
    Dim strAcell As String
     
    If Not Intersect(Target, Range("B9:B43")) Is Nothing Then
        i = Target.Row
        intws1 = i - 3
        intws2 = i - 2
        intBcell = i - 8
        strCcell = ”S” & i - 8
        strAcell = “A” & i + 61
         
        If Target.Value = "" Then
             
            Target.Value = intBcell
            Target.Offset(0, 2).Value = "N"
            Worksheets(intws1).Name = Target.Offset(0, 1).Value & Target.Value 'Rename Student Report Card worksheet to Default Name
            Worksheets(intws2).Name = Target.Offset(0, 1).Value & Target.Value & "C" 'Rename Student Checklist worksheet to default name
            Range(strAcell).Value = "" 'Remove Report Card Name & Checklist Name
            Worksheets(2).Range(strAcell) = "" 'Remove Vocab Name
             
            If Target.Offset(0, 1).Value = strCcell Then
                 
                Target.Offset(0, 2) = "N"
                Worksheets(intws1).Name = Target.Offset(0, 1).Value & intBcell 'Rename Student Report Card worksheet to Student name
                Worksheets(intws2).Name = Target.Offset(0, 1).Value & strCcell 'Rename Student Checklist worksheet to Student name
                Range(strAcell).Value = "" 'Remove Report Card Name & Checklist Name
                Worksheets(2).Range(strAcell) = "" 'Remvoe Vocab Name
            Else
                 
                Target.Offset(0, 2) = "Y"
                Worksheets(intws1).Name = Target.Value & " " & Target.Offset(0, 1).Value 'Rename Student Report Card worksheet to Student name
                Worksheets(intws2).Name = Target.Value & " " & Target.Offset(0, 1).Value & " Check" 'Rename Student Checklist worksheet to Student name
                Range(strAcell).Value = Target.Value & ", " & Target.Offset(0, 1).Value 'Assign Report Card Name & Checklist Name
                Worksheets(2).Range(strAcell) = Target.Value & ", " & Target.Offset(0, 1).Value 'Assign Vocab Name
            End If
        End If
    Else
    If Not Intersect(Target, Range("C9:C43")) Is Nothing Then
    i = Target.Row
        intws1 = i - 3
        intws2 = i - 2
        intBcell = i - 8
        strCcell = ”S” & i - 8
        strAcell = “A” & i + 61
         


        If Target.Value = "" Then
             
            Target.Value = strCcell
            Target.Offset(0, 1).Value = "N"
            Worksheets(intws1).Name = Target.Value & intBcell 'Rename Student Report Card worksheet to Default Name
            Worksheets(intws2).Name = Target.Value & intBcell & "C" 'Rename Student Checklist worksheet to default name
            Range(strAcell).Value = "" 'Remove Report Card Name & Checklist Name
            Worksheets(2).Range(strAcell) = "" 'Remove Vocab Name
        ElseIf Range(TargetCell).Value = intBcell Then
             
            Target.Offset(0, 1).Value = "N"
            Worksheets(intws1).Name = strCcell & Target.Offset(0, -1).Value 'Rename Student Report Card worksheet to Default Name
            Worksheets(intws2).Name = strCcell & Target.Offset(0, -1).Value & "C" 'Rename Student Checklist worksheet to default name
            Range(strAcell).Value = "" 'Remove Report Card Name & Checklist Name
            Worksheets(2).Range(strAcell) = "" 'Remove Vocab Name
        Else
             
            Worksheets(intws1).Name = Target.Offset(0, -1).Value & " " & Target.Value 'Rename Student Report Card worksheet to Student name
            Worksheets(intws2).Name = Target.Offset(0, -1).Value & " " & Target.Value & " Check" 'Rename Student Checklist worksheet to Student name
            Target.Offset(0, 1).Value = "Y"
            Range(strAcell).Value = Target.Offset(0, -1).Value & ", " & Target.Value 'Assign Report Card Name & Checklist Name
            Worksheets(2).Range(strAcell) = Target.Offset(0, -1).Value & ", " & Target.Value 'Assign Vocab Name
        End If
    End If
End Function