Who coined the name "tensor" and why? What does the word "tensor" really mean, not the mathematical definition?
I think the OP referes to the modern meaning of the word, in which case, according to that website, it first appeared in german physicist Woldemar Voigt's paper Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung published in 1898. (I do not have access to this paper, but probably this deals with deformation tensors in crystals).
A tensor muscle is a muscle that stretches some part of the body, e.g. the tensor veli palatini or tensor tympani. The word ultimately derives from the Latin tendere meaning "to stretch", see Douglas Harper's etymonline.
Hamilton first introduced the term to mathematics; see its entry in "Earliest Known Uses of Some of the Words of Mathematics".