The Boeing 720 was a modification of the Boeing 707. Why was it given the unusual number of "720" instead of a "707-xxx" or "7x7" designation?
Because the launch customer, United Airlines wanted it. From Boeing frontiers:
The 720 was a ... first marketed to the airlines as the model 707-020. United Airlines was very interested in the 707-020 but had previously decided to go with Douglas and the DC-8. To help United avoid any negative public relations for going back to the 707, Boeing changed the name of the 707-020 to the 720.
According to aviationweek, the name change was at the behest of William ‘Pat’ Patterson, the president of launch customer United Airlines.
The 720 first flew before the 727 project began. At that time, there was no "7x7 series" – just the 707.
(The 717 passenger plane didn't come along until the 1990s, though the internal Boeing model number of what are usually called the C-135 Stratolifter and KC-135 Stratotanker was also 717, and that did exist at the time the 720 was produced.)