The Bubbloid 554 was originally called Bubbloid112. It was designed by Carl Hoff and is the result of a collaboration between Cubewerkz and Calvin's Puzzles. Bubbloid puzzles are corner turning Cuboids that do not shape shift.
Each number in the original naming convention refers to the number of shared edges between 2 adjacent corners sharing that edge.
For example, on the big square face, 1 edge piece is shared between 2 adjacent corners. On the shorter edge, 2 edge pieces are shared between 2 adjacent corners.
That is how the number 112 comes about. To make it easier, the naming was changed to count the corner and edge pieces of the 3 sides, thus the name Bubboid 554.