From personal experience, you should probably wait until the two of you decide to make things more official or things start to get serious before you tell your parents.
When I was younger, I've told my parents about all the people I've pursued. Almost all of them were a bust which just made my parents think that I probably shouldn't date anymore, that dating is bad, and that I'm overly focused on my love life instead of my studies. Then I took the approach I mentioned above and only told them about the ones that have at least gotten to the more serious stage and they now only occasionally tell me that I'm overly focused on my love life (rather than before where they told me that all the time). I mean it could also be because now I'm older but I'd like to think that it's because they no longer think I'm overly "easy" or "desperate". Believe me, I'm still "desperate" in the sense that I continue to have unsuccessful crushes (like normal people do, which they don't believe is true for whatever reason and thus they have labeled me as desperate and easy), however they no longer know that and therefore they are less likely to give me a hard time about it. Unless you're fine with your parents giving you a hard time about dating, only tell them about the ones that are serious.
However, if your parents seem to be pretty chill about dating and understand that it's normal that they can be unsuccessful, then it may be fine for you to tell them. I'm just saying that if your parents are anything like mine (where they were each other's first everything and never had to date and/or they believe dating is one of the many the downfalls of modern society), follow my personal approach as it's easier to appear like you're playing under their rules rather than changing their rules.