How to save shape groups as photo to fileDialog path with amended name

It may solve the problem. It is not tried fully as Final Export method is throwing PowerPoint converter installation problem in my present system. But otherwise there is no error like "Compile error: Method or data member not found"

May simply try collection

Option Base 1 
'
'
' then in Declaration
Dim FileName As New Collection
Dim FilePath As New Collection
Dim FinalName As String
'
'
'the in For Each vrtSelectedItem In .SelectedItems

            FileName.Add fso.GetBaseName(vrtSelectedItem)
            FilePath.Add fso.GetParentFolderName(vrtSelectedItem)
'
'
'
' then in For i = 1 To numPics after End With

    FinalName = FilePath(i) & "\" & FileName(i) & "_with logo"
    ActivePresentation.Slides(i).Select
    'MsgBox FinalName
    ActivePresentation.Slides(i).Export FinalName , ppShapeFormatJPG, 3072

Could not understand if you are placing earlier saved pictures in slides and placing logo on them? if it is that simple then may try simpler alternative with single loop

Sub saveWithLogo()
Dim fd As FileDialog
Dim directory As String
Dim vrtSelectedItem As Variant
Dim osld As Slide
Dim oPic As Shape
Dim osldGroup As Slide
Dim oshp As Shape
Dim logoPic As Shape
Dim i As Integer
Dim num_pics As Integer
Dim fso As New FileSystemObject
Dim FileName As String
Dim FilePath As String

Set fd = Application.FileDialog(msoFileDialogFilePicker)
With fd     'Get pictures from file dialog, add logo to each picture
If .Show = -1 Then
   For Each vrtSelectedItem In .SelectedItems
   numPics = .SelectedItems.Count
   FileName = fso.GetBaseName(vrtSelectedItem)
   FilePath = fso.GetParentFolderName(vrtSelectedItem)
   Set osld = ActivePresentation.Slides.Add(ActivePresentation.Slides.Count + 1, ppLayoutBlank)
   Set oPic = osld.Shapes.AddPicture(vrtSelectedItem, msoFalse, msoTrue, 50, 50)
   osldno = ActivePresentation.Slides.Count
   logoWidth = 6.18 * 28.3
   logoHeight = 1.4 * 28.3
   Set logoPic = osld.Shapes.AddPicture("C:\foxpro2\vtools\logo.bmp", lsoFalse, msoTrue, 50, 50, logoWidth, logoHeight)
    osld.Select
    ActiveWindow.Selection.Unselect
        For Each oshp In osld.Shapes
        If oshp.Type = msoPicture Then oshp.Select Replace:=False
        Next oshp
        With ActiveWindow.Selection.ShapeRange
        If .Count > 1 Then .Group
        End With
        FinalName = FilePath & "\" & FileName & "_with logo"
        'MsgBox FinalName
   osld.Export FinalName & "_with logo", ppShapeFormatJPG ' , 3072
   Next vrtSelectedItem
   End If
End With

Set fd = Nothing
End Sub

For the curios or those with the same problem. Here's the final successful macro with what I learned from Ahmed's Answer.

I added image scaling since the output size was way smaller than the original.

Sub saveWithLogo()

Dim fd As FileDialog
Dim directory As String
Dim vrtSelectedItem As Variant
Dim osld As Slide
Dim oPic As Shape
Dim osldGroup As Slide
Dim oshp As Shape
Dim logoPic As Shape
Dim i As Integer
Dim num_pics As Integer
Dim fso As New FileSystemObject
Dim fileName As New Collection
Dim filePath As New Collection
Dim finalName As String

Set fd = Application.FileDialog(msoFileDialogFilePicker)
With fd     'Get pictures from file dialog, add logo to each picture
    If .Show = -1 Then
        For Each vrtSelectedItem In .SelectedItems
            numPics = .SelectedItems.Count
            fileName.Add fso.GetBaseName(vrtSelectedItem)
            filePath.Add fso.GetParentFolderName(vrtSelectedItem)
            Set osld = ActivePresentation.Slides.Add(ActivePresentation.Slides.Count + 1, ppLayoutBlank)
            Set oPic = osld.Shapes.AddPicture(vrtSelectedItem, msoFalse, msoTrue, 50, 50)
            With oPic
                .LockAspectRatio = msoTrue
                .ScaleWidth 1.875, msoTrue
            End With
            logoWidth = 6.18 * 28.3
            logoHeight = 1.4 * 28.3
            Set logoPic = osld.Shapes.AddPicture("C:\Pictures\Logo Images\" & "logo.png", lsoFalse, msoTrue, 100, 85, logoWidth, logoHeight)
            With logoPic
                .LockAspectRatio = msoTrue
                .ScaleWidth 0.005 * oPic.Width, msoTrue
            End With
            Set oPic = Nothing
            Set logoPic = Nothing
        Next vrtSelectedItem
    End If
End With

For i = 1 To numPics    'Groups pictures on slide
    Set osldGroup = ActivePresentation.Slides(i)
    ActivePresentation.Slides(i).Select
    ActiveWindow.Selection.Unselect
    For Each oshp In osldGroup.Shapes
    If oshp.Type = msoPicture Then oshp.Select Replace:=False
    Next oshp
    With ActiveWindow.Selection.ShapeRange
    If .Count > 1 Then
    .Group
    End If
    End With
Next i

Dim ap As Presentation: Set ap = ActivePresentation
Dim sl As Slide
Dim shGroup As ShapeRange
For Each sl In ap.Slides
    ActiveWindow.View.GotoSlide (sl.SlideIndex)
    sl.Shapes.SelectAll
    Set shGroup = ActiveWindow.Selection.ShapeRange
    shGroup.Export filePath(sl.SlideIndex) & "\" & fileName(sl.SlideIndex) & "_with logo" & ".jpg", ppShapeFormatJPG, , , ppScaleXY
Next

Set fd = Nothing
Dim v As Long
For v = 1 To Application.ActivePresentation.Slides.Count
    ActivePresentation.Slides.Range(1).Delete
Next v

End Sub