Name for a retractable spring
A quick search for "tape measure spring" resulted in a list of various products, but also included the term "recoil spring." Changing the search term to "recoil spring" really threw a wrench in the works, however, as some of the returns presented items related to gun-type weapons.

More appropriate to the question is that recoil spring also appears when dealing with pull-start engine mechanisms. As with a tape measure, extending the spring loaded portion (starter rope, tape measure, etc.) causes the recoil spring to tighten up, providing the retraction force in the expected and desired manner.