If 19961 is the oldest citation the OED can come up with, "slash"
really is a coinage of the computer age. Yet the character had
been in algebra books for centuries. The oral tradition that underlies
eqn would be the authority for a "solid" name. I suspect, though,
that regardless of what the algebra books called it, the name
would be "divided by".
This is sheer hypothesis, but I have always thought that \ got
onto printer chains and type balls as a crude drawing aid. Ditto
for |. Once the characters became available people began to find
uses for them.