Helix with a helix as its axis

According to this journal article, we may call it a doubly-twisted helix or generally a multiply-twisted helix.

For a light bulb the wire is called a "coiled coil filament" in this Wikipedia article.

The German word is "Doppelwendel" (roughly translated: double screw).

I don't believe there is a standard term. Nevertheless, MathWorld calls the resulting curve a "slinky".

Of course, one can have a "slinky" of a "slinky":

A corresponding construction on the torus is called an "iterated torus knot", so perhaps "iterated helix" would be a good name. I don't know of any standard name.