As mentioned above, they do indeed have databases, though it might take a brave (careeless) payor to be willing to assume the payee just from name similarity. There ARE more similarities available to raise the confidence of success though: the first coming to mind being the account number structure of different businesses being different, often, so even though there might be six electric companies with names similar enough, the account number structure you give (say, 182-996-736-2-3 or ###-###-###-#-#) could make it pretty certain a particular one is right. Your location might be a good second "similarity" and your checkwriting history with the payor (if a bank) might well be a solid third. Lots of others one wagers too. And they might even immediately send a query to all concerned and base their payment on the replies. Though none of that might be helpful for a payment to a florist.
More importantly, it is a cheap way for them to seek business and this likely plays a role. As a business, we receive payments like this perhaps 10 times a month (manufacturer, so not doing 12,000 transactions a month like a video store might (have)). And EVERY single one of them contains a "Come, COME TO ME little one, come to me and gain all the (non-)benefits of using this same service!" And EVERY last one of them contains a "Come to our website and sign up to receive these payments via ACH which will certainly not arrive sooner like we want to imply as we simply won't send them until later... but will be hideously cheaper for us than these paper... things... you are getting now!"
EVERY single one, even after receiving a dozen already.
So yeah, might be a paper check the first time or two, but they work hard on shifting you to sending the required information so they can ACH it. Why do they not just ask the originator? Well, getting that kind of information presents a barrier to entry, eh? Even a mild one is still a barrier. And there's no interacting via ACH so there is no obtaining the payee as a (probably bigger) user of the service.
And the other big reason for desiring the payee as a customer is that many of these services, and ALL of them that work through a credit card in some way or another, try to sell you on a credit line to float the checks. For many the lack of actual benefit and high costs vs. their own paper checks or ACH's is not a problem if credit they cannot otherwise obtain, or only obtain after climbing significant barriers to entry with, say, banks, is offered along with it.
Those markets are why these services make it as easy as possible, and then even easier, even dangerous, for the low-level payee to engage them. Costs are still minimal compared to possible gains.
And not one of them would EVER have the least problem holding your money a week or two trying to resolve a payment difficulty, then simply "returning" it (i.e.: NOT returning it, but netting it from their draw for some upcoming batch... of course), leaving you holding the bag and having to explain your mortgage payment not arriving, with late fees now tacked on and so on.
Like someone said though, the ACH system is hilariously antiquated. Not that it is the active reason for anything here, but it certainly limits the supply of these service providers to predators.
