Since he is a European Aristocrat, then the EuroAristo naming standards should be followed. https://www.wikitree.com/wiki/Help:Name_Fields_for_European_Aristocrats
So Laval, as first name and preferred name, with EuroAristo naming, the titles go in the nickname field - so this should be Graf von Nugent, titles don't go in the prefix field.
Nugent then should be his Last Name at Birth. The question of what to put in his Current Last Name and Other Last Names is a bit of a puzzle. I'm not totally sure why Wikipedia gives his name as Nugent von Westmeath, in one of the sources, he is just Nugent, and in another the family name is given as Nugent-Westmeath.
I think in English we would refer to him as Nugent of the family of the Earls of Westmeath, but this wouldn't have any affect on his name, but in German this probably equates to Nugent von Westmeath? Perhaps that as his Current Last Name and Nugent-Westmeath as Other Last Name?