I Where does the name of XY model come from?

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Why is the XY model in statistical physics called so?
 
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Are you interested in the physical reasons or the historical reasons of the origin of the name?

The spin vectors have two components in this model, so it is quite natural to call it the XY-model.

From E. Lieb et al., "Two soluble models of an antiferromagnetic chain", Annals of Physics 16, 407 (1961):
"Because the Hamiltonian only involves the x- and y- components of the spin operators, we call this model the XY- model."

This might be one of the first papers, where the model actually carried this particular name, but I am not exactly sure about that.
 
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