My husband gave this mystery flower a compliment. He said it looks like “a real flower.” That is, it looks something that a person might deliberately grow in a garden. I agree that it’s pretty, but it reminds me a little bit of Mystery Flower #1, which I found growing in a yard with poor-quality soil, so it may be just another weed.
My best guess at the identity of this mystery flower is in the comments.
This is almost certainly Ajuga reptans, a..k.a. ajuga, blue bugle or bugleweed. And some people do deliberately grow it in gardens. I read that ajuga likes moist soil and shade, two things that we have in abundance here, and it also attracts butterflies, so I say it’s a keeper. Since it is just sprouting randomly in the backyard, I am thinking of transplanting some of it to my rock garden. Why pay for flowers when you can get them for free, right?