I'm having a hysterectomy soon. Will this cause menopause?

Not by itself. A hysterectomy, or removal of the uterus, will not cause menopause or other hormone changes. If the ovaries are removed at the same time, then menopause will result. The ovaries are responsible for producing female hormones.
Depends on ovary. Hysterectomy is removal of uterus. If they take out your ovary (you have 2 ovaries in body) if both are removed you can have menopause. Usually they leave one ovary in during hysterectomy - if this is done for bleeding issues instead of problem with ovary like cyst etc so if you have one ovary no you would not have menopause if you removed both ovaries with uterus then yes you would have menopause.