Function getFileName(ByVal path As String) As String
    Dim cM As Integer
    cM = InStrRev(path, "\") + 1
    If cM = 0 Then Exit Function
    getFileName = Mid(path, cM)
End Function
 

la api es una de las mas compactas, pero es la mas lenta, aca paso una optimizacion de la que puso ignorantev1.1 , es unos 300 milisegundos mas rapida.

Function getFileName(ByVal path As String) As String
    getFileName = Mid$(path, InStrRev(path, "\") + 1)
End Function

Function nombre_archivo(ByVal Ruta As String) As String
Dim partes() As String
partes = Split(Ruta, "\")
nombre_archivo = partes(UBound(partes))
End Function

Seguramente no es la mas rapida ni por asomo xD

Esta pregunta la he hecho unas 450 veces pero se me olvida 

Como medimos la velocidad?

@seba123neo
Jajajajaja te barriste con tu segunda funcion 

con la clase CTiming, la podes bajar de aca:

CTiming

aca va el codigo, con las funciones posteadas hasta ahora. pongan un boton en el form y este codigo.

Option Explicit
 
Private CTiming As CTiming
 
Private Declare Function GetFileTitle Lib "comdlg32.dll" Alias "GetFileTitleA" (ByVal lpszFile As String, ByVal lpszTitle As String, ByVal cbBuf As Integer) As Integer
Private Declare Sub PathStripPath Lib "shlwapi.dll" Alias "PathStripPathA" (ByVal pszPath As String)
 
Const Path As String = "C:\Documents and Settings\Llamazares\Mis documentos\Downloads\SexoDeRanas.avi"
 
Dim i As Long
Dim ValTest As Long
Dim vres As String
 
Private Sub Command1_Click()
    Me.Print "Test de velocidad" & vbCrLf
 
    ValTest = 10000
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = StripPath(Path)
    Next
 
    Me.Print "seba123neo api: " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = GetFileName(Path)
    Next
 
    Me.Print "ignorantev1.1: " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = getFileName2(Path)
    Next
 
    Me.Print "seba123neo (ignorantev1.1): " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = Fn7913(Path)
    Next
 
    Me.Print "79137913: " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = nombre_archivo(Path)
    Next
 
    Me.Print "grester43hck: " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = GetFileMrFrog(Path)
    Next
 
    Me.Print "Mr. Frog ©: " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = GetFileName123(Path)
    Next
 
    Me.Print "seba123neo (segunda): " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = SacarFilenameE_C(Path)
    Next
 
    Me.Print "Elemental Code: " & CTiming.sElapsed
 
    CTiming.Reset
 
    For i = 0 To ValTest
        vres = SacarFilenameE_Cv2(Path)
    Next
 
    Me.Print "Elemental Code 2: " & CTiming.sElapsed
 
End Sub
 
Private Sub Form_Load()
    Set CTiming = New CTiming
    Me.AutoRedraw = True
End Sub
 
Private Function StripPath(ByVal sPath As String) As String
   Call PathStripPath(sPath)
   StripPath = sPath
End Function
 
Private Function getFileName2(ByVal Path As String) As String
    getFileName2 = Mid$(Path, InStrRev(Path, "\") + 1)
End Function
 
Private Function GetFileName(ByVal Path As String) As String
    Dim cM As Integer
    cM = InStrRev(Path, "\") + 1
    If cM = 0 Then Exit Function
    GetFileName = Mid(Path, cM)
End Function
 
Private Function Fn7913(ByVal sPath As String) As String
    Dim Buffer As String
    Buffer = String(255, 0)
    GetFileTitle sPath, Buffer, Len(Buffer)
    Fn7913 = Left$(Buffer, InStr(1, Buffer, Chr$(0)) - 1)
 End Function
 
Private Function nombre_archivo(ByVal Ruta As String) As String
    Dim partes() As String
    partes = Split(Ruta, "\")
    nombre_archivo = partes(UBound(partes))
End Function
 
Public Static Function GetFileMrFrog(ByRef sFile As String) As String
    GetFileMrFrog = RightB$(sFile, LenB(sFile) - InStrB(sFile, "\") - 1)
End Function
 
Public Function GetFileName123(ByRef vPath As String) As String
    GetFileName123 = Right$(vPath, Len(vPath) - InStrRev(vPath, "\"))
End Function
 
Public Function SacarFilenameE_C(ByRef sPath As String) As String
    SacarFilenameE_C = StrReverse(Left(StrReverse(sPath), InStr(1, StrReverse(sPath), "\", vbBinaryCompare) - 1))
End Function
 
Public Function SacarFilenameE_Cv2(ByRef sPath As String) As String
    SacarFilenameE_Cv2 = Right(sPath, Len(sPath) - InStrRev(sPath, "\", Len(sPath), vbBinaryCompare))
End Function
 

PD: no vi que era con la clase modificada de Mr. Frog © , pero me imagino que no hay diferencia no ?

saludos.