I've been there a few times but always referred to it as "Monkey Mountain", never knew it was called Takasakiyama. If you're in Beppu it's well worth a visit.
Well, you had to figure it was named something in Japanese, right?
高崎山 appears to mean "tall, mountainous mountain". Monkeys aren't mentioned, though the name of the monkey preserve, 高崎山自然動物園 "Mount Takasaki Nature Zoo", does mention animals.
https://www.japan-guide.com/e/e4703.html
Bear in mind that these are wild animals and that there are days where the park's closed due to no monkeys.