When does new sprint start

The open assessment question is based on words from the Scrum Guide:

A new Sprint starts immediately after the conclusion of the previous Sprint.

The timing of the events is also there:

All the work necessary to achieve the Product Goal, including Sprint Planning, Daily Scrums, Sprint Review, and Sprint Retrospective, happen within Sprints.

and

Sprint Planning initiates the Sprint by laying out the work to be performed for the Sprint.

and

The Sprint Retrospective concludes the Sprint.

The point is that there shouldn't be an extended period of time between the Sprint Retrospective (which follows the Sprint Review, in relatively short order) and the Sprint Planning. The exact timing depends on the nature of the team and organization.

Consider the maximum timebox for the events: 4 hours for Sprint Review, 3 hours for Sprint Retrospective, and 8 hours for Sprint Planning. That could mean up to 15 hours for these events that bookend a Sprint. Even a colocated team working the exact same hours couldn't do that in a single day, so there is going to be clock time between the end of the Sprint Retrospective and the start of Sprint Planning. If your team is not colocated, has structured the events to allow for more stakeholder participation (especially in the Sprint Review), or otherwise has working hours that don't overlap, these events could be spread over 3 days.

The key point is to minimize the working hours between the Sprint Retrospective and the Sprint Planning. During this time, the team has not crafted a Sprint Goal, selected Product Backlog Items for the Sprint, or developed a plan for completing those Product Backlog Items. I've found that if you do have working hours between the events, the best use of time is for non-product work. This could be company-related overhead (mandatory paperwork, training, etc.) or skill development to make the team members more cross-functional.

If you keep the time between Sprint Retrospective and Sprint Planning minimized, there's no need to have any special name for the period between them.

Sprint Planning initiates the Sprint by laying out the work to be performed for the Sprint.

That describes how it initiates it. It doesn't initiate the Sprint by starting it.

The Sprint boundary provides a sublime moment of transparency when it is absolutely clear what work has been Done and what work has not been Done. Any gap between Sprints would reduce transparency by providing places to hide.

Hence there can be no gaps; when one Sprint ends the next starts less than a micro-second later. You could not slide a cigarette paper between Sprints.