I love the name MoonDragon. His is what we have all been waiting for and more than justifies the funding of commercial flights to ISS. Well done Elon and all at SpaceX
I've always preferred "Silver Dragon" - fits with the convention set by Red Dragon (not that SpaceX has ever made themselves beholden to naming conventions), and sounds somewhat like "Selenic" (synonym for "Lunar"). But it's their spaceship and they can call it what they want.
This can mean only one thing: SPACE SEX! (And that would be science, wouldn't it??)
If you really want that, it's best to keep to LEO, in order to keep costs down - that is, unless you need a good shot with the Earth in one of the windows. Point is, if that isn't happening on ho-hum LEO flights right now, it's not gonna happen on the first manned flight to the moon in over 4 decades.
Anyways, regarding test flights, there are really only 4 "new" things about this mission (compared to the manned ISS demo): Dv2 riding on FH, BLEO navigation, van Allen Belts, and Re-entry heat. SpaceX has already shown good rad tolerance on Dragon, so I don't think that's something to be worried about. BLEO navigation will be new, but also shouldn't be a major challenge. Dv2 riding on FH will require testing, but it's testing they were already doing for Red Dragon, and it won't be too different from riding on F9 - if it does cause problems, though, they'll be during ascent, when powered abort is possible.
This leaves re-entry heating. I know they'll be running all the CFD they can, and watching the demo missions to make sure those heat shields perform as expected, but still... This is the one issue that seems to me like it really would require an unmanned shakedown. Everything else is relatively low-risk, or can be tested during demo missions, but for this reason alone, an extra test mission up front might be important. Plus, it might send a message to NASA about crewed firsts, though the circumstances are quite different.