Anytime Fitness has a tattoo room at its corporate headquarters in Woodbury, Minn., with a chair, a sink and a book illustrating ways that employees can show off the company’s running man logo.

While job-hopping is rampant, a surprising number of American workers are expressing a bond with their employers in permanent ink. Employees at such companies as tech’s Red Hat Inc. and sportswear icon Nike Inc. have brand logos plastered on their ankles, shoulders and arms.

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