I've only been able to trace it back to Asimov's "Foundation" series, first started in 1942. Anyone know if this trend of currency naming goes back any further?
[Edit: completely rewritten, February 13, 2021.]
The term "credit" meaning "a unit of currency" goes back at least to the early 1930s. The following information is from the Historical Dictionary of Science Fiction.
1934: The earliest known citation is from Astounding Stories, December 1934, in part 1 of the serialization of The Mightiest Machine, a novel by John W. Campbell, Jr., available at the Internet Archive. Quoting from p. 23, col. 1:
"Right enough, and tell me why I have to build that five-million-credit flying laboratory," demanded Spencer.
1931: There are slightly earlier citations for the form "credit unit", the earliest being from The Birth of a New Republic, a novel by Miles J. Breuer, M.D. and Jack Williamson in Amazing Stories Quarterly, Winter 1931, available at the Internet Archive. Quoting from p. 25, col. 1:
On the following day, the Assembly met again, made an appropriation of five million credit units to defray the expenses of the war, and issued a call for volunteers to fight for the freedom of the planet.
The first instance of "credits" is in the 1888 novel "Looking Backward 2000-1887" by Edward Bellamy. This is both the first time money is referred to as "credits" in scifi (though they are called both "credits" and "dollars") and the first time an abstract "digital" currency is described in scifi. Specifically, the story features the first scifi description of what we would now call a "debit card", though they are actually called "credit cards" in the novel. Describing a Marxist utopia, all citizens receive an equal amount of credits from the state, represented on a punch card. No physical money is in circulation.
A credit corresponding to his share of the annual product of the nation is given to every citizen on the public books at the beginning of each year, and a credit card issued him with which he procures at the public storehouses, found in every community, whatever he desires whenever he desires it. This arrangement, you will see, totally obviates the necessity for business transactions of any sort between individuals and consumers. Perhaps you would like to see what our credit cards are like.
"You observe," he pursued as I was curiously examining the piece of pasteboard he gave me, "that this card is issued for a certain number of dollars. We have kept the old word, but not the substance. The term, as we use it, answers to no real thing, but merely serves as an algebraical symbol for comparing the values of products with one another. For this purpose they are all priced in dollars and cents, just as in your day. The value of what I procure on this card is checked off by the clerk, who pricks out of these tiers of squares the price of what I order."
Note that the punch-cards alluded to here was not a scifi prediction of early computers, but had already been a real-world technology for 150 years before the book was published [2,3].