The Mocha Conundrum

So I hate Starbucks. They were starting to grow on me after several enjoyable knitting sessions, but that was all undone when I took a break from work today.
I was cold at work, which is unusual as the tech room it a tiny, dust filled triangle lopped off the corner of the store, with a closed door and no ventilation, and 3-10 computers running constantly. It's always hot. In the summer it was the hottest place in the store.
But today I was cold. As I walked past the receiving bay to clock out, I saw the receiving dock was wide open, even though there was no truck at the door.
"It's you causing this cold Ben!"
"It's not me! There's a man here who was apparently sent to remove dead animals from under the dock."
Anyway, I wanted a warm drink (and I don't drink coffee), and the only food places within a minute walk from work are Starbucks, Superstore, a hotdog stand outside Superstore, Safeway, and the Starbucks inside Safeway. So it really had to be Starbucks.
"Can I have a medium hot chocolate, please?"
"Pre-made, or our Signature Series?"
"What's the difference?"
(There was some talking about syrups and brewing processes and organic milk or something)
"Pre-made"
"What size?"
"Medium"
"Tall?"
(reluctantly) "Sure"
She punched "Tall Signature Series" into the till, and charged me $4.25
What I got was a cup of something that didn't taste much like hot chocolate at all and had a load of white foamy stuff on top that ended up on my nose, and no lid (which makes me nervous about putting it down on the bench at work).

At Tim Horton's, if I ask for a medium hot chocolate, the lady says, "That'll be $1.12 please", and hands me a cup of hot chocolate that tastes exactly like hot chocolate tastes, it doesn't end up on my nose, and has a lid, and cost one quarter as much.

Tim Horton's was directly opposite us when I worked at Sneakers. When I'd got to get the guys coffee, Jeff would have a mocha. You know how I feel about all this coffee lingo. I'd watch the lady fill the cup half with coffee and half with hot chocolate. Why don't they just call it what it is rather than coming up with a fancy name?

But then I came to the Mocha Conundrum.
Mocha is an unnecessary word - common words can be used to say the same thing.
"Mocha" is one word; "half coffee and half hot chocolate" is lots.
It's easier to say "mocha", but it's easier to understand "half hot chocolate and half coffee".
I like simple names for things, but I don't like long names, so which should it be?
I think the beverage should be eradicated all together. Who'd ruin hot chocolate by putting coffee in it anyway?