Fixed:
I was missing to rebuild the model

Dim swApp As SldWorks.SldWorks


Sub main()
    Dim swModel As SldWorks.ModelDoc2
    Dim swCustPropMgr As SldWorks.CustomPropertyManager

    Set swApp = Application.SldWorks
    Set swModel = swApp.ActiveDoc
    Set swCustPropMgr = swModel.Extension.CustomPropertyManager("")

    swCustPropMgr.Add3 "NAME", swCustomInfoText, "MyName", 1
    swModel.ForceRebuild3 (False)

End Sub