The hoods are one of the under-appreciated wear parts on your bike. Consider that they're polymers, which are known to eventually degrade, in part due to exposure to ultraviolet light. I recently replaced a pair of R8000 hoods after about 3 years of heavy use, and they were starting to slip off my levers. FYI, Shimano calls them bracket covers. Hoods or hood covers should be easily understood at LBSes, at least in the US.
Peter wrote that you can sometimes find a shifter model which uses the same hoods. This will require some inside knowledge on the part of yourself, a mechanic, or some helpful person on a forum. For example, R8000 and R7000 can share hoods, but not with R9100. Furthermore, the hydraulic brake + mech shifting levers can't share hoods with the rim brake + mech shifting levers, or the Di2 + hydraulic levers, etc. For Campagnolo, in the 2000s, all the 10s levers would share the same hood, and I think the same was true for all 9s levers. But things diverged a bit since then, especially with the introduction of hydraulic brakes, plus the introduction and then withdrawal of Potenza and Athena.
Aside from searching eBay or AliExpress for original replacements, you can be open to the possibility of third party replacements. For example, ODI Grips has the Hudz lineup of replacement hoods for some shifters (e.g. Shimano 7900 and earlier, two versions of Campy). I believe these were regarded as decent.
If you search AliExpress, you may also find low-cost third party manufacturers of hoods for older levers. I found at least one listing for ST-2300/3400 hoods. Especially with the stuff on AliExpress, it's possible the quality won't be as good as the original part, or they won't fit as tightly - that's not a reflection on mainland China per se, but that in making cheap replacements, something has to give, and tolerances and material quality are two good bets. Returns may also be logistically more challenging.
In any case, at some point, finding third party replacements may be your only option, as manufacturers may eventually discontinue production. For example, I unsuccessfully searched for replacement hoods for Dura Ace 7400 and 7700 levers. Yes, these are old, with 7700 going out of service in 2004. However, they were the top of the line group. There wasn't an obvious listing for OEM 7970 hoods (first generation Dura Ace Di2), although I did see one for 6870 hoods (first generation Ultegra Di2).
As a related anecdote, I found replacement pads for the interior of an older Giro model on Amazon.com. This was the Giro Prolight, probably made around 2014, but I shopped for the replacement pads in 2018 when they'd discontinued the pads. At the time, I didn't realize the difference between OEM material and third party manufacturers. I think that for this ad, it was clear, but sometimes the ads are misleading or at least not clear. Anyway, they did fit the helmet, but they were much thicker than the original pads. They were tolerably decent.