Anyone seriously planning on doing this or anything like it would be well advised to consult a good trademark lawyer with the specifics. Specifics will matter in such a case. That said:
Under US trademark law, the key question is whether a reasonable person would be confused into assuming that there is some connection, and that the new firm could be relied on based on the reputation of the old one. if so, this is a trademark infringement unless permission is obtained from the trademark holder (not likely to be granted). Since "orbitz" is a coined term its protection is stronger, there is no natural object or concept this can refer to. "AppleMoving" is less likely to be confused with "Apple Computers" because apples are real things and need not refer to computers.
The likelihood of confusion depends on the specific facts of an individual case.
Note also that trademark protection is a matter of private civil lawsuits. If orbitz didn't choose to sue for whatever reason, nothing would have stopped OrbitzMoving.