Just format after convert to a date (tested in SQL Server v.2017)
dd/mon/yyyy
Select Format(cast('25/jun/2013' as date),'dd/MMM/yyyy')
dd/mm/yyyy
Select Format(cast('25/jun/2013' as date),'dd/MM/yyyy')
dd/Month/yyyy
Select Format(cast('25/jun/2013' as date),'dd/MMMM/yyyy')