Hex key
A hex key, also known as an Allen, hex-head or zeta key or wrench, is a tool used to drive screws and bolts that have a hexagonal socket in the head.
This tool is also commonly referred to by various trademarks or brand names. "Allen wrench" was originally a trademark of the Allen Manufacturing Company in Hartford, Connecticut, taken out in 1943. In non-English speaking parts of Europe, it is usually known as an "Unbrako key" (often misspelled "Umbrako"), which is a brand name established in 1911. The brand is owned by SPS Technologies. In Germany and the Netherlands, this type of screw is known by the name "Inbus", after the company that patented them in 1936, Bauer & Schaurte Karcher in Neuss (Innensechskantschraube Bauer und Schaurte). (It is still known as an Inbus-key—often misspelled as Imbus-key—in parts of Europe.)
wikipedia

I would always write it capitalized because it is (or was) a company name as it is also capitalized in German as a brand, btw.

Thank you very much for the fast and detailed answer!
Would you rather use the term "hex key" or is "Allen key" the more appropriate / common one?

In AE, I have only ever heard it called an Allen wrench.

Personally I would always call it an Allen key or like girly-girl said, Allen wrench. It was called hex key on the wiki page, but I don't know who calls it that, maybe people in the business? But everyone I know (mostly people who aren't into building things) would only know of it as an Allen.

Ignoramuses like me always thought they were called Ikea keys.

@schraubt noch - that would be understandable, but for Americans like me who had never been lucky enough to live within 500 miles of an Ikea there needed to be another name!