I answered the puzzle you linked and of course I used reverse image search to identify the persons. This post has gotten rather long and blathery, so here's the synopsis up front:
Solvers may use reverse image search, but it's not a very interesting puzzle mechanic. If a designer wants to prevent reverse image search, the puzzle must make sure that an image search does not provide the answer.
Your question has two angles. First, from a solver's perspective: In my opinion, this puzzle screams "use reverse image search to identify the persons". The portraits are the only information we have and the depicted people are not really well known. I mean, I know that Rossini was an Italian composer of operas, but I don't know what he looked like. I had no chance of identifying the other three.
Reverse image search exists and it is the ideal tool to identify people from digital portraits. Cropping and uploading the images is tedious legwork. If you don't enjoy that, skip the puzzle.
Many puzzles have a knowledge element that requires some research. Some of them, such as country codes, capitals or chemical symbols, are puzzle staples, but still may require you to look up some data on Wikipedia. Others delve into obscure regions of knowledge and are research fests.
Research can be fun, but I don't enjoy the routine of doing reverse image search. In the case of the linked puzzle, there were only four images to identify, but if there are many images to identify, I'm usually put off the puzzle. (Occasionally, like in this here puzzle, I can take advantage of other people's reserach work posted in partial aswers. I'd never have gone through the trouble of identifying all these people, and I could't identify any of them from their photos. I couldn't identify some by their names, even.)
Second, from a designer's perspective: I don't think you can avoid that solvers use image search. Putting a moral ban on image search – "Please do not use image search" – will only draw the solvers' attention to it.
(Other types of puzzles, notably those tagged grid-deduction and no-compters, make it obligatory to write a detailed description of how the solution was arrived at. Well, I'm not particularly good at grid deduction puzzles, but having to write a scientific paper with many images puts me off answering these instantly. That doesn't mean that I don't try to solve the puzzle, but I sure would loathe to document my solving.)
Anyway, if you want to prevent solvers from using reverse image search, make the puzzle inaccessable to search. Your question mentions giving the names of the people outright, but there are other means:
Use images, but modify them, so that they are recognizable, but look completely diferent to a search engine. Just blurring may not do the job, but I can imagine that a different colour palette as in Andy Warhol's work or in Obama's Hope poster will work. There may even be online image filters for that.
Provide the information by other means, for example as text. "Composer of the 'Barber of Seville'" may be too obvious – if you don't know the answer already, it's also just a simple web search –, but perhaps you can find some aspect that makes the research more interesting. It may be necessary to provide some means of confirmation, for example the letter count (9, 7) for Gioachino Rossini. (But that will make people use that letter count in reverse word solvers like Qat or One look, of course.)
Another strategy, especially if you have many related things, is to make some of these things easy to find or even obvious, so that you can find the rest via a common link. That's not possible in the puzzle you linked, though.