What is the origin of the names P-1 and P-2 of nickel boride catalysts?
The actual differences between the two forms are well-documented on Wikipedia. As for the names: as far as I can tell, the choice of "1" and "2" seems to be arbitrary. The choice of the letter "P", though, is described by C. A. Brown (who carried out investigations into the synthesis and reactivity of these catalysts).1,2 In footnote 13 of reference 1, Brown writes:


  The designations are derived from Purdue University, where this work was initiated.


So, it is within reason to assume that the P stands for Purdue.



References


Brown, C. A. Catalytic hydrogenation. V. Reaction of sodium borohydride with aqueous nickel salts. P-1 nickel boride, a convenient, highly active nickel hydrogenation catalyst. J. Org. Chem. 1970, 35 (6), 1900–1904. DOI: 10.1021/jo00831a039.
Brown, C. A.; Ahuja, V. K. Catalytic hydrogenation. VI. Reaction of sodium borohydride with nickel salts in ethanol solution. P-2 Nickel, a highly convenient, new, selective hydrogenation catalyst with great sensitivity to substrate structure. J. Org. Chem. 1973, 38 (12), 2226–2230. DOI: 10.1021/jo00952a024.