It is an "old man cactus" (called a "viejito" in its native lands)... I am not great with cacti, but look at Cephalocereus (the old man of Mexico) and Oreocereus (the old man of the Andes). All of these plants will grow brighter and lusher fur with lots of sun, and go correspondingly hairless in low light. Your plant looks excellent to me.
Old Man of Mexico (Cephalocereus senilis)
If you look at other pictures on the net you will find a few green plants without much hair (probably indoor or greenhouse grown)... these are useful for identification because they show you how many ribs the plant has and where the spines are distributed. You might not be able to see the spines on your plant very well, but you should be able to feel them well enough to know if it's a match.
3 viejitos here for illustration. Middle one is Cephalocereus (closeup of crown above).
Your Euphorbia could be (?) Euphorbia heptagona which apparently is the new name for a plant I know as E. enopla. Take a look at some pictures.