Its called Miranda, as all of he moons in this system have names from Shakespeare or Spenser. From the looks of it, it should have been called 'Frankenstein'.
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The tilt of the Uranian axis would have to be from either some gradual evo of its orbit, or from an impact; if it had been from an encounter with a large body going by (and Uranus is 15 times the mass of the Earth, so, it would have to be a whopper) the Uranian moons would show some goofyiness — which is the case with Neptune, and Neptune is even more massive.
Actually, there is a third possibility — the atmosphere of Uranus could have arrived later, perpendicular to the plane of the solar ecliptic; the arrival of such a mass could have knocked Uranus into a different orientation, and while it could seem like a one in a kajillion shot, it would explain the (mostly) undisturbed orbits of the moons and may be the best explanation.
Of course, this assumes that the moons were in orbit around Uranus in the first place.
A fourth possibility is, previously the moons were in orbit around a gas giant; the whole works bumped into Uranus, which was just the solid core of what exists today. Some of the original moons were lost because they were on the business end of the transaction, but the gas giant would have been less massive and therefore the moons would have been further out.
And of course, some of them might have been lost anyway, and wound up as part of the core.
And that could mean that the proto-Uranus got its axis tipped right then, if it hadn’t been before.
A fifth possibility is, the Uranian moons were not around at the time of the axis getting tipped, but were acquired later, through capture, and still a long time ago. Or perhaps, the capture of the moons is what tipped the axis in the first place. Aha! ;’)