Putnam certainly deserves credit for the colorful realization, but philosophically brain in a vat/isolated brain issues are traced back (including by SEP) to Cartesian evil demon , which predates not only Putnam, the Matrix and other modern implementations of non-stop hallucinations, but even 1812 and Frankenstein. Even before Descartes Avicenna's Floating Man thought experiment imagined an "isolated mind" scenario, although not for the purpose of pervasive deception of demon-fooled or envatted brains, but rather for another Cartesian purpose, disembodied minds, with a man
"created at a stroke, fully developed and perfectly formed but with his vision shrouded from perceiving all external objects - created floating in the air or in the space, not buffeted by any perceptible current of the air that supports him, his limbs separated and kept out of contact with one another, so that they do not feel each feel".
The roots of the pervasive doubt and radical skepticism, symbolized by the envatted brains, are as old as the roots of philosophy itself. If you really dig into it the grandfather of Putnam's vats and Descartes's demons is the Plato's cave, where Plato restricted mental options of his prisoners as best as he could imagine in his low-tech times, by tying their hands and immobilizing their necks so they could be deceived into taking reality to consist of dancing shadows on the wall, cast by the fire behind them. Plato himself was of course inspired by Parmenides and Zeno. In fact, Plato raises the very same issue about the shift in meaning of terms that became central to Putnam's analysis of envatted brains:"And if they could talk to one another, don’t you think they’d suppose that the names they used applied to the things they see passing before them?" Plato, like Putnam, answers "no", i.e. brains raised in a vat have different meaning of "brain" or "vat" than us, same as how Plato's prisoners have the wrong meaning of "real things", unless they listen to Plato.
After Putnam's 1981 entry Cohen and Lehrer (1983) put a new spin on the problem, sometimes distinguished as the "new evil demon" problem, which focuses not on externalism of meaning but on reliability of justification and the notion of knowledge:
"By bracketing the skeptical worries, it seems that many of your beliefs about the external world constitute knowledge. As your counterpart is systematically deceived, her beliefs about the external world do not constitute knowledge. Moreover, it seems that while you might suppose that your beliefs are produced by processes that can reliably lead you to the truth, the means by which your counterpart arrives at her beliefs are wholly unreliable... it seems the reliabilist ought to say that your counterpart’s beliefs are not justified. However, many would consider that position to be strongly counterintuitive. They are convinced that while your counterpart knows nothing, your counterpart is no less justified in her beliefs than you are in yours".
And this of course also goes back to Plato and his K=JTB (Knowledge is Justified True Belief), the "new" is the old in a new garb. This is one of those cases where one comes to appreciate Whitehead's quip:"The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato".