Linda,
the name Bornemissza is meaning: "who do not drink wine"
There were a lot of famous Bornemissza families, noblemen or not.
The most famous Bornemissza was Bornemissza Gergely(Gregor) in the 16th Century, leutenant thent captain of fort Eger. You can read about him by a very nice novel, written by Géza Gárdonyi: "The Eclipse of the Crescent Moon" (you can buy that for example in a Canadian bookshop:
http://www.pannonia.ca/)
The poet Bornemissza, Péter, was also famous, he lived in the same age. He was one of the poets, who developed the poetry in Hungarian language (till that age the poets used the Latin language usually)
Especially among the housewifes was very popular Anna Bornemissza, who wrote the first cookery book in Hungarian language at 1630.
There are some other baron Bornemissza, who are not really Hungarians, eg the Thissen-Bornemissza, but if I were you, I would be proud of the earlier three Bornemisszas.
By the way, all of families have the same legends, eg in my family is told, that we are relatives of king Mathias's mother. So, in the next, please, tell me: "him Majestic, Lajos" OK?
Lajos Reich, Hungary.