Just one end seem to be enough. But some GMs may think differently.
I'd say just to one end. It happens to bring the other end with it.
This is one of those common-sense moments. I'd have to say any DM forcing you to enchant both ends is being very, very punitive.
I would look at it this way; there was a 3.5e ability you could apply for very little, which would make a weapon glow like a torch. That's it. No combat applicability, just that you'd drop something like 500gp and your weapon glowed.
So what... you're going to tell your player "sorry, only one end of your double-sword glows, so you can't actually see by that light. You need twice as much light as anyone else." No.
The called ability should work even if it has to drag a little "dead" weapon with it. It's like using teleport and getting to take your clothes with you for free.
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A double weapon is a single item, and a single weapon. You can wield a double weapon as if you were fighting with two weapons, and the rules say they are considered to be separate for the purpose of enhancing them, but it's one item. If you are disarmed of it, you lose both ends. If it's sundered/shattered, you lose both. If one end is a calling weapon, it can be summoned to your hand.
+1 for citing some rules, rather than using a "it just makes sense" argument.
Definitely this - a double weapon is still a single weapon, even though it lets you strike with either end (enhanced separately).