Don't know the true backstory. I know it helps us differentiate (up here it's Go Cougs for Washington State which is in the vicinity).
I would love to know the official story on how we got to "Coog".
Good question; ever since I've been following (going back to the early 80's), it's always been Coogs. Can't find anything online about it.
Might have just been a pronunciation thing as Coug doesn't look like it makes the same sound as Coog.
Vague memory of that being answered on the previous rendition of the coogfans web site.
Site is long dead Purged by scout.