The classic logo is often on the can/bottle near the nutritional information: http://imgur.com/OHinuge (from a can of Diet Coke in the UK, taken today. The can was part of a large multi-pack case).
The smallest responsive version of the logo says "coke", rather than "coca-cola", which I've not seen before. I couldn't see any use of "coke" by itself, when used for "diet coke" they use a different style: http://www.amodelrecommends.com/wp-content/uploads/2011/02/d...