I have posted twice before (and see also) about whether it is better to say or write, for example, Gyeongbokgung, Gyeongbokgung Palace or Gyeongbok Palace. We have more choices with mountains because we can put mount(ain) before or after the name: Namsan, Namsan Mountain, Nam Mountain, Mount Namsan. One possibility I didn’t suggest was Mount Nam, because I’d never encountered it, but recently I did, in a blog I can’t name because I’ve forgotten which of several I’ve been browsing recently it was. For some reason, Mount Nam looks and sounds wrong, but Mount Halla and Mount Seorak look and sound reasonable. It might be that Nam is monosyllabic, but nearby where I went to high school was Mount Brown.
A movie review mentioned a tv series named Jirisan. Wikipedia’s page on the tv series is named Jirisan (TV series) but refers to Mount Jiri throughout, while its page on the mountain is named Jirisan and refers to Jirisan, except for two fleeting references to ‘Mt. Jiri’. But I shouldn’t (indeed can’t) expect consistency from Wikipedia.
Ultimately, there’s no ideal solution. The simplest is to use Gyeongbokgung and Jirisan, but using Gyeongbokgung Palace and Jirisan Mountain is more helpful. In fact, the most helpful is “Gyeongbokgung, a palace near the centre of Seoul”, and “Jirisan, a mountain in the south of Korea”, but you wouldn’t want to do that every time. A lot depends on your intended listeners/readers.