I feel it is likely that the phrase in question is a way of rendering "with honours" in Latin. The link below provides some possible contexts. Grammatically 'aucto' goes with 'nomine' (the distance from it being no obstacle, in my view). 'Nomen Baccalaurei in Rebus Machinalibus' is the plain bachelor's degree, but for those with honours it is enhanced ('auctum') by the Degree/Step of Honour. The capitalization of 'Honoris Gradu' suggests that we have a formal definition of status here. Otherwise the phrase 'honoris gradu aucto' could conceivably be taken as an ablative absolute, as has been suggested, meaning something like 'raising the level of his dignity', but that would be an unnecessary flourish.

I wonder if the awarding body does in fact deal in degrees with honours.