Saddle of lamb is the traditional name in United Kingdom. Outside that tradition, butchers carry comparable lamb cuts under different names — sometimes the same anatomical piece, sometimes a close cousin. The alternatives below are grouped by country so you can match what your local butcher actually carries.
Same anatomy: a saddle is both loins attached as one roast; a loin chop is a cross-cut single-loin slice from that same section. Saddle is the whole, chops are the divisions.
Anatomically adjacent — rack is the rib end (8 ribs), saddle is the loin section behind it. A whole rack-plus-saddle is sometimes called a *long saddle* or sold as a guard-of-honour preparation.