A word of caution about the name and approach. You'll find when fundraising that branding yourself as "ycreject.com" will make it very hard to raise funding. VCs and Angels are going to think, "if YC wouldn't give them money, why should I give them a much larger amount of money?"
I don't think it's controversial to say that most angels and VCs suffer from group-think and an over-reliance on social proof. That's why finding your first investor is the hardest.
This concept will be perfect for boot-strapers, but not good for someone looking for funding. You'd be better off avoiding all relation to YC and branding yourself as some sort of unaffiliated startup co-op.
It shows determination in the same way that showing up on a date and telling him / her that 'I'm having a lot of success in the dating world, I just got turned down for 3 dates' projects confidence. Sure, you're out there getting names and numbers and seeing what happens, and that's great! But what's the story you're telling to potential investors / spouses?
The name YCRejects can tell a lot of stories. "We had an interview, but we weren't the right fit for the program, so we're building the product / finding the market ourselves" is one story. But the name YCRejects says "We didn't get an interview, but..." and puts you [in my mind] in an awkward position where you're apologizing and making excuses for applying to something. That's not right.
If YCombinator brought this idea together [as it obviously has], why not build on that? YCombinator — Summer Batch 2.
You're a group of founders, brought together by YCombinator, working together to build awesome things. You're a skunkworks incubator. You [probably] have no funding, but you have passion for your ideas and a burning desire and determination to get this show started.
It's just a name by itself for now (for SEO purposes as well). Of course I wouldn't go around to investors and say we're 2nd tier groups that PG didn't want.
Right now, I want to keep it very small. Find out what everybody wants and go from there.
Dissociated from YC could totally work!!! Also find mentors to answer questions at the dinner, and have each team do a 5 minute quick presentation regarding their progress that week. Also, don't judge people on any other criteria outside of a) launch date (to be sure you're all planning on lunching something substantial around the same time) and b) potential to become profitable soon.
I don't think it's controversial to say that most angels and VCs suffer from group-think and an over-reliance on social proof. That's why finding your first investor is the hardest.
This concept will be perfect for boot-strapers, but not good for someone looking for funding. You'd be better off avoiding all relation to YC and branding yourself as some sort of unaffiliated startup co-op.