Yes, that has been on my mind for a while and this thread could hardly be a clearer indicator.

What should it be called? What day should it go out?

If you do make it monthly, my recommendation is posting it on the 15th of every month, to stagger it with the other regular threads. This way you don't make the start of the month a scramble of postings.

For sure it should be counter-cyclical with Who Is Hiring, but I was wondering if maybe it would be good to put on weekends.

Mondays could also work, since it would allow people an extra weekend to finish what they want to show. Also it will allow them to procrastinate at work.

I'd say the Saturday after the paycheck closest to the 15th. People on bi-weekly pay schedules have funds again and it's counter cyclical to the 'Who's Hiring' threads.

The list of bi-weekly paychecks for 2020 is here: https://www.nfc.usda.gov/Publications/Forms/1217n_20.pdf

Meaning that June's thread should be on the 20th. July on the 18th. August on the 15th. September on the 12th. October on the 10th.

Sunday seems like a good day

Sunday might be good because then the question "what are you working on" is associated with what you might be working on over the weekend, i.e. things you're doing for curiosity, fun, or obsession, rather than a workaday job.

Second or third Sunday, evening.

Perhaps: Ask HN: What are you making?

Something side-project specific might be better, lest it becomes a list of pitches!

How about at the end of every month?

So, people who start working on something new at the beginning of the month are ready to talk about their projects

It reminds me of Idea sunday / Project weekend or something like that

Idea sunday never worked very well. A thread about things people are actually working on should be more interesting.