Think about things from the point of view of someone who has never used Reddit or the fediverse, but you've heard about them both from recent news articles and want to see what they are about.
Reddit:- You Google Reddit and your first result is Reddit.com. You click the link and are presented with the front page. You from scroll from a few hours and end up signing up and staying.
Lemmy:- You Google Lemmy and your first result is a wiki article for Lemmy Kilmister... Your second result might be join-lemmy.org, which you're smart enough to realise it's probably more likely what the news is about.
You click join-lemmy.org and are presented with a page of information about the fediverse, links to set up a server and pictures of code...
There is very little chance you're going to investigate further.
If we want the fediverse to replace Reddit then either
A) Lemmy needs to improve its initial impression and Search engine optimization
B) We should be promoting a different platform with a better initial first impression.
I'd recommend kbin personally as it gives the same sort of experience as Reddit from the initial interaction.
You're absolutely right that we have a bit of a terminology issue here, but one slightly advanced and techy thing to understand about the fediverse is that the fediverse itself is the "platform":
Lemmy, Kbin, Mastodon, Calckey, etc., are software projects or processes that are running on some server somewhere, and ActivityPub is the protocol (kind of like a language) that all these processes use (to varying degrees) to speak with each other. As users, we interact with a specific server or service (like beehaw.org or kbin.social) that is running that software and sharing info with other servers through a protocol.
This is totally different to Reddit or Twitter, which are both the names of the service AND (probably, but we don't now) the software that the service is running behind the scenes. Naturally that makes it a bit easier to talk about, because we don't have any access to or knowledge about the software or protocols that they use, and we can just talk about the services.
This is all a long-winded way of saying that Kbin and Lemmy are replacements for Reddit (the software) while servers like kbin.social or beehaw.org are replacements for Reddit.com (the service), except they also talk to each other somewhat seamlessly. I'm logged into the server "kbin.social", which runs a software called "Kbin", which communicates over a protocol called "ActivityPub" to a bunch of users who are on other servers running other software.
In other words, Google searching for "Lemmy" isn't exactly a good metric, not only because Reddit is one of the biggest websites around and Google knows this, but also because "Lemmy" isn't the actual name of the service that we are using right now, just the software. If you tell someone to go over to a specific server (like beehaw.org, kbin.social, etc.) then they'll have a much easier time finding something that they can actually use.
Most of us are guilty of kind of glossing over all this stuff to keep things simple and easy to understand, but there are some layers of nuance to the fediverse here that make this a little bit more complicated than you're making it out to be imo.