In a Nutshell:
Whilst the issue is disputed amongst the scholars, with some arguing it is obligatory to send blessings on the Prophet (saw) whenever his name is mentioned, and others arguing it is recommended, the strongest position based on all the evidences available to us is it is recommended (mandoub) and not obligatory.
Whilst it is not obliged to send blessings upon the Prophet (saw) when his name is mentioned, it is highly recommended and good etiquette for Muslims. It is seen as a bad habit for refusing to do so and a form of miserliness.