You have a few other problems. To see the format for saving, try recording a macro. The other problem is in the makeup of the filename. In Windows, "/" and "\" are paths to folders. When using dates with slash characters, either use Format() to reformat the date to a string or Replace() to replace a string's characters that cause the problem.
Use F8 to debug code one line at a time. Another way is by debug.print and view code in the Immediate Window. e.g.
Sub SaveInvWithNewName()
Dim NewFn As Variant, pDT As String
'Copy invoice to a new workbook
'ActiveSheet.Copy
pDT = CreateObject("WScript.Shell").SpecialFolders("Desktop") & Application.PathSeparator
If Dir(pDT) = "" Then
MsgBox "Path does not exist:" & vbLf & pDT, vbExclamation, "Macro Ending"
Exit Sub
End If
NewFn = "C:\Users\nebojsa\Desktop\FakturaKraj\Fakt" & "--" & Range("F11").Value & "--" & Range("F15").Value & "--" & Range("F16").Value & ".xlsx"
Debug.Print NewFn
Exit Sub
ActiveWorkbook.SaveAs NewFn, FileFormat:=xlOpenXMLWorkbook
ActiveWorkbook.Close
NextInvoice
End Sub