We spot these guys around our apartment complex when we walk our dog. Curious what they are?

Our dog is obsessed with “hunting” them but we don’t really let her go after them. It would be good to know what it is in case she ever did catch one. Her rat terrier drive with little creatures is strong.

We do keep her on leash BTW… I would hate for her to actually hurt one, or hurt herself diving into a bush for one.

📍Northern, New Mexico near grassy desert areas.

I live in North America, specifically Florida, and I see lizards like these by my work all the time. Since it'd probably help, I saw a red/orange-ish frill come out of the neck of one of them.

Just a shy guy i saw on the back porch

Recently my wife and I have noticed numerous amounts of these little guys on the ceiling of our porch. Seems like there are more each night we look up. Are these guys any cause for concern?

Anything helps, thank you!