The 'Kenmeri' Name was for the C110 range of Skylines and is not GT-R specific, it is reference to the advertising campaign used for the C110 Skyline, it contained a happy young couple by the names of Ken & Mary cruising around in their new C110, the ads were so adored by the Japanese that it bought about the nickname you could even buy figurines with a wee C110. (I've attached an image). I believe the ads started before the C110 range but the C110 got the nickname from them.
The 'Hakosuka' was also a nickname used, given to the C10 range of Skylines the range that included the very first GT-R the PGC10 2000GT-R. Loosely translated is something along the lines of Boxed-shape Skyline.
The DR30 Group. 5 Super Silhouette Race car had the nickname 'Deppa' which was in reference to the metre long flames it would spit out of it's exhaust during racing.
Oh!! and the DR30 RS-X also had the nickname 'Iron Mask' for obvious reasons.
"Iron Mask" from the TV Drama In Japan ... Cheers!