There was no model explicitly named "after Elite." The Elite (2007–2010) was the final revision of the original Xbox 360 chassis. Microsoft then released a completely redesigned console:
The Elite (120GB/250GB, HDMI, black matte, chrome trim) was the premium original model. The S/Slime rendered it obsolete by fixing RRoD, adding Wi-Fi, and shrinking the footprint. If you have an Elite, it's a collector's piece—but for playing, an S or E is far more reliable.