I also would love an ID. One of those box store Salvia labels, that was about it. Hardy to at least zone 8. I assume

Salvia greggii

https://salvias.org.au/pruning-propagation-of-salvias-information/

" Some People like to 'nick/ wound' the stem, which helps to promote roots at this point, white others just cover a section of stem and wait for it to root, or bury nodes ( or elbows) – these nodes naturally form roots when they touch the ground"

Well, I've wounded it, so maybe that's the route ;)

You could get lots of plants from that piece. Smaller bits root better than larger branches. I'd strip off all the side shoots. You should get 8 or 10 cuttings.

So where would you cut it? Or are you just using the green shoots?

Maybe it might help: even though I have gardened for decades and decades... I only just started propagating about 5 years ago. This past season I started trying all kinds of things. I don't claim to be an expert, and I'm really willing to learn something new 🥰

I would trim off each side shoot. Or you could take heel cuttings by simply stripping off the side shoots by hand. Little 2 - 3 inch cuttings take quite fast. My photos of Salvia cuttings are on a different device but this article pretty much covers it. https://www.theguardian.com/lifeandstyle/2018/sep/22/how-to-create-new-plants-for-free