I plan to take the SATs in June and then retaking it in October. I think my June score will be around 1250 or less. I don't feel that confident because I neglected studying and didn't find out about PrepScholar until now. That's why I plan to retake the test in October. I would have more time to study and I think I can work my way up to a 1500+ score with smart studying.
The thing is, I heard the colleges like Yale and UPenn require all of your SAT scores to be sent instead of allowing superscoring. According to a PrepScholar article I read, this can negatively affect me because the college will sees ALL of my scores - good and bad. If I get a mediocre score the first time I take the SAT but a way better score the second time, isn't that good because it shows improvement? Or should I just take the SAT once in October, when I'm confident?
If you're not confident in your ability to do well on the June SAT and it's not a financial hardship, you should cancel the June test date. It sounds like you already know you want to apply to schools that require all of your test scores, and you're planning to do more serious study to prepare for the October SAT. While it's true that schools like seeing improvement from test to test, it's much better to just get the high score the first time around.
The only reason not to cancel your June SAT and just take the October SAT is if you are planning on applying early decision or early action to any school; if so, your October SAT scores may not get to the school in time, leaving your application incomplete. But other than Early Action/Early Decision, there's really no reason to take a test you know you're not going to do well on when you'll have to send those scores to colleges you're applying to.
For a deeper dive into consistency and standardized test-taking, read my answer about retaking the ACT for consistency.