Is it possible to have menopause after a hysterectomy but still have 1 ovary and age 24?

Yes. Although 1 ovary is usually able to function quite well and prevent early menopause, it is possible that it is has stopped functioning. If you are having menopausal symptoms like hot flashes and night sweats, you should see your gynecologist who can order blood tests to check the amount of hormones you are making.
VERY UNLIKELY, but.. After hysterectomy it is difficult to tell when menopause occurs without the cessation of periods to alert the woman. Most women 'go through' menopause in late 40's-early 50's so it would be very unlikely for you to be menopausal @ 24. Since 1 ovary was removed and one remains it is possible the remaining ovary is low functioning. Lab tests (fsh/lh) would be elevated in premature ovarian failure.