It is a filler flower used in floristry.
I would say it is Limonium capsia, L. sinensis or L. carolinianum, all of which are used in the floral industry. They are also called sea lavender.
Hello, Your article says when digging Sea Lavender, “dig deep,” my Question is just how deep? I have two side by side but want to move one of them. Thank you.
None of the sources I found said "how deep" but that the roots grow long and delicate and can be easily damaged. One source said if they are damaged they may die and shouldn't be moved.
You might rethink moving one.