The phenomenon of turning a noun into a verb is very common. Some are more well known, like "shouldering the blame" or "tabling a discussion," while others are newer and less known. I just came across "when it storms." Is there a real name for this or is it just called "verbing?" If not, what was it called before the word "verbing" was coined?
The phenomenon of verbing spans several other, slightly broader phenomena - some of which intersect or are subsets of one another.
Anthimeria is the rhetorical use of a word as if it were a member of a different word class. I would expect that most examples of verbing begin as rhetorical devices.
Conversion, also called zero derivation, is the creation of a word from an existing word without any change in form. ("I will table this")
If a new word is formed "(I am tabling this") this is an example of derivation, the process of forming a new word on the basis of an existing word
Because changing the class of a word changes the syntax of the word, all of these are examples of a functional shift, which occurs when an existing word takes on a new syntactic function.
So it would appear that there isn't a term synonymous with "verbing" that was used before that term was coined, but I would expect one or more of the above would have been used to describe the phenomenon.
Of course the word "verbing" is itself an example of verbing!
The OED cites "verbify" from 1878 and "verb" as a verb from 1936.
Linguists have the adjective (and sometimes noun) "deverbal" to mean a word that has been formed from a verb.
Note that in many languages verbing requires some morphological change to the word because verbs have a different shape from other words. In English, content words do not show their role by their shape, so you can often verb a noun without any change to it (as there).