I have something similar growing in one of my planting beds where there is a bird feeder. This does get a small blue flower and I simply keep pulling it and the birds keep replanting it. Just keep mechanically removing it and composting it since that will add some needed nutrients to your compost.

Tired of pulling it, and not interested in composting it just to let critters reseed my yard with this thing. I want to kill it and make it go away. I want to know what this is so I can make sure it's on the kill list of any herbicide I get.

Looks like Commelina sp.

Since birds bring seeds for many weeds into your yard spraying some kind of "weed" killer around really does not do much except make you feel as if you have done something. Spraying does not "get rid" of anything except the "weeds" currently growing that can be very easily dispatched by mechanical means at much less cost. Within a short period of time the birds will seed new "weeds" that will then also need to be sprayed, and on ad infinitum, adding to the pollution of our world.

Looks like a member of the 'wandering jew' family, tradescantia. RoundUp is the only way to get rid of it if it is widespread, but it may come back quickly so don't consider it eradicated after one spraying. I have actually seen this for sale often at garden centers.