I've never heard it referred to as Monkey Grass, but it's often called Lily Turf - it is, indeed, Liriope muscari variegata, or one of the variegated hybrids, and you should leave it alone until spring, then cut back just as growth outdoors begins. If the new leaves are arriving, take care not to cut those back - it's only any old leaves from this year you need to cut down. You don't have to cut it back, it'll still grow just fine, it just looks tidier if you remove the older leaves - they often look tatty after winter and won't look any better if you leave them in place, they tend to shrivel and go brown as spring progresses.
This plant is not a grass at all, but a perennial, sometimes classed as a sub shrub although it isn't, usually evergreen in all except very hard winters. More info here
UPDATE: following your comment, there's nothing to be gained by cutting the flowers off, so if you just want to do that for display in a vase or something, fine, but it doesn't increase the flowering if you do cut them. Left on the plant the flower stems may form black berries which are decorative in themselves, and provide food for birds. Regarding the name monkey grass, it's probably just another common name, many plants have more than one!