So Ansgar is the masculine form, Asgard the feminine, and they both mean God + protection. I don't know if the German version of Wiki is as demented on the topic of name meanings as the English, but this seems sane enough!
Asgard, however, as far as I know is the place where the Norse gods lived, so it's originally an address, not a name. I'd always connected it, rather vaguely, with the great World Ash tree so it would be something like Ash(tree) protection. But I'm no Norse scholar!