The name Moctezuma (also commonly used is Montezuma) or Motecuhzoma, is a name from the central Mexican language of Nahuatl, referring to a lordly frown. Many people vaguely relate it to the last emperor of the Aztecs, but that's not only vague but inaccurate.
Technically, the last emperor was Cuauhtémoc, though it could be argued that by the time he took the throne the empire was in shambles and he wasn't a true emperor. But if we're going to talk about Aztec rulers, scholars today use the term Moctezuma for more than one.
Otherwise known as Moctezuma I, he ruled from 1440-1469. He was the 5th tlatoani, or ruler in Tenochtitlán (more about Aztec government). This ruler did a lot to consolidate the Aztec civilization, and to expand its borders. During his rule, the empire stretched to the Gulf of Mexico. In the triple alliance of three great cities, Tenochtitlán began to solidify its place as the "capitol city". He led a successful campaign against the Mixtec peoples. He led the construction of the Chapultepec aqueduct, which was completed in 1466 after 13 years of labour.
Motecuhzoma Ilhuicamina's half brother, Tlacaelel, may have held a lot of the true power at this time. The emperor consulted him about everything. Both were able military leaders, and Tlacaelel acted as a military and political advisor to the emperor and other important nobles.
During this time the Templo Mayor, or the Temple to Huitzilopochtli, was greatly expanded. Thousands of slaves from all over the territory controlled by the Aztecs were made to work on the temple. Conquered peoples provided sacrifices, and the resources for the great structure.
The laws of the civilization of central Mexico were further developed at this time, clarifying the different roles in society.
The name Ilhuicamina means archer of the sky, or the one who shoots arrows at the sky. There has been some question about what he was actually called in his lifetime. Some evidence supports the theory that he never went by the name Moctezuma (Motecuhzoma) at all, but only Ilhuicamina. Seeing history as cyclical (it repeats), the post-conquest Mexica peoples may have renamed him, feeling it was fitting for the first and last great rulers of a dynasty to have the same name. Susan D. Gillespie has written about this.
He has also been called Huehuemotecuhzoma, or Old Moctezuma, to differentiate him from the emperor we will talk about next.
Otherwise known as Motecuhzoma II, this is the ruler that most people think of when they hear the name. He was made especially memorable to history because he ruled at the coming of the Spanish. His handling of the initial clash of cultures has been the source of endless debate.
Also known as Motecuhzoma the Younger (the meaning of Xocoyotzin being honoured younger one), in comparison with his famous relative, he was also an able military leader. He was the 9th ruler in Tenochtitlan, ruling from about 1502 to 1520.
You can read all about Moctezuma II here.