Low income housing question about employment

Please upvote! I'm really trying to get out of my situation, I am applying to jobs and low income housing because the environment is no longer safe for me mentally. It's part of why I was on unemployment during that time.

I was on unemployment for 6 months end of 2024. As soon as my unemployment ended I began door dashing. I'm still new to it, but I am making money.

So I have pay stubs for June 2024 - December 2024 and then pay stubs for DoorDash in January 2025. Would low income housing accept this for employment verification?

Also, I'm staying at my siblings place right now, would it be a bad idea to put them as my landlord if we have the same last name?