Yes, the Benedictines (and Cistercians among others) have their own LOTH. The basic structure is the same, but the psalm order and number of psalms is different. And this has been the case for 1500 years.
After Vatican II, new approved and licit schemas were devised. Currently there are four major ones but many communities or congregations have their own, approved through proper authority.
The four are:
Schema A, which is the same schema as described by St. Benedict in his rule; it is 1500 years old, and has a couple of new options available to distribute the psalms of Prime at other hours.
Schema B (which the abbey I’m associated with uses), first defined in the 1960s; it distributes the entire psalter over one week (with a couple of two-week options)
Schema C and D, dividing the psalter over 2 weeks.
Also some communities with extensive external apostolates may use the Roman LOTH (4-weeks), and we oblates (at least at our abbey) are free to use either the abbey’s schema or the LOTH.