My yard has a plant that is extremely robust, needs no water and wants to reseed all over. My neighbor says her former tenant bought it at a native plant sale. My neighbor has removed it from her yard and I'm guessing she would like it if I did too. I had been trying to cut off all the blooming upright spikes this year. I like the plants because they stay green all year. The flwering spikes produce lovely bright dark red berries. It's a great screen for not so nice fence and I've pruned one into a tree shape that will screen our neighbor's back porch. I keep chopping it back but it keeps producing and will go to seed soon.
Trying to Identify Plant
Certified GKH Gardening Expert
The closest plant that I can find that fits this image is call Teucrium Canadense.
There are many cultivators and several leaf shapes. Flowers vary in color and the berries or fruit can be white or red.
It is consider invasive which also fits your description.