I don’t know the name but I have done and was told it’s an very invasive plant. It is pretty but be careful. I pulled some to shape the bed. I threw the discarded plants on the ground after a week in the sun and almost pure clay ground it’s still green and shows no signs of shock or dying.

Thank you for these very good followup photos. The flowers & buds are look like those of mallow type (Malva). I’m still leaning toward either the species M. sylvestris (common mallow, French hollyhock, tall mallow, etc…) or one of its cultivars. Copy and paste the included link below for information. Click on images to enlarge. Best wishes!

https://en.wikipedia.org/wiki/Malva_sylvestris