On Jan 24, 6:00*pm, Higgs Boson wrote:.

Anybody know the name?

Also, is it safe to cut it back?

Might be a euphoria variety , say a rigida. If so, it cleans up easy
& easy to propragate, take the one on the right you snapped off on and
put it into a glass of water, roots fairly quickly. A good seedling
mix will work also if you pay attention to the moisture. Be cautious
of the sap. Repot the poor thing with a well draining mix w/ alittle
N.
Google images for euphoria rigida, gopher plant for detail info