Can I change the dates of a sprint after it has started?

Yes, you can change the dates whenever you want, such as when you are extending a sprint.

Note that if you have specified the available time for the teams as totals in the sprint, and you change the duration, the ideal line (the gray dotted line) in the burndown chart will redistribute that time across all days in the new duration of the sprint. This is probably not what you want. In that case, you can switch to specifying the available time individually for each day in the sprint. To do that, open the popup dialog for each team in the sprint, and click the link "Specify for each day instead":