From the context (of course), especially from 世界で, 格闘技と名前のつくものの大会 and かならず.
Her grandfather gave money generously to martial arts(all kind of things/sports that are called/categorized as martial arts) competitions held in all over the world (e.g. Jūdō competition in Japan, Taekwondo competition in Korea, Capoeira competition in Brazil, Sambo competition in Russia, etc, etc), and his name was always added to the titles of those competitions (e.g. 城戸光政杯東京国際柔道選手権 "Kido Mitsumasa Cup Tokyo International Judo Tournament").
Can you see how and where your interpretation is wrong?