As n.m. notes in a comment below the posted question, one standard name for such set-aside time is "20 percent time." An article by Ed Frauenheim in Workforce Management dated May 2, 2006, and titled "On the Clock But Off on Their Own: Pet-project Programs Set to Gain Wider Acceptance" includes this paragraph:
At a handful of companies, though, employees are effectively guaranteed they can pursue projects they are itching to explore. Google puts it in writing right on its Web site about life as an engineer at the Internet giant: "Google engineers all have '20 percent time' in which they're free to pursue projects they're passionate about."
The PDF version of this article is available here.
The term (and underlying concept) evidently goes back at least to 1959, as is evident from this excerpt from Creativity, an Examination of the Creative Process: A Report to the Third Communications Conference of the Art Directors Club of New York (1959):
Some of you who are in administrative positions may be interested in the tangible dollars-and-cents results of this 20 percent policy. Just a few years ago, a chemical engineer, working on 20 percent time, developed a process now used in our operation. He started research on 20 percent time because he was trying what he thought was a long shot. He had a hunch— and, incidentally, the scientific method does not preclude the use of hunches— and he succeeded in getting men in other scientific disciplines to help him on their 20 percent time. Early work showed the symptoms of success and, to make a very long story short, within a period of about six months the project became formalized and he had time to put his 20 percent of time elsewhere. ... The skill is, in part, being able to recognize the lucky break. So the completely-directed scientist will not be able to pursue what he may feel is a bit of luck, unless he has a bit of extra, unregulated time.