If a person has 'Oxon' after their name, it means they have been awarded a degree by the University of Oxford (presumably a law degree for a barrister, although this has no impact on the 'oxon' suffix).
For future reference, 'Dunelm' after someone's name means they did their degree at Durham and 'Exon' means they did it at Exeter. I think there are only a few universities in the country who are allowed to do that Although I think the best response to this came from one of my friends, who said 'does that mean that a Liverpool John Moores graduate is obliged to put 'Moron' after their name?!'