I have Lamiastrum galobdeon with the yellow flower spikes. It can be incredibly invasive given enough moisture. And it is not easy to pull as it roots at every node. We have about an acre of it covering our leach bed. It is beginning to escape down into the woods which concerns me as it will choke out everything in its path.

The newer hybrid lamiums might be less invasive but I would start with a small amount and keep an eye on it.

Here are less invasive species for groundcover in shade
European Ginger
Canadian Ginger
Solomons Seals - there are many types
Epimediums
dwarf hostas - if you want a truly dense groundcover this will do it. Just keep dividing and replanting every 2-3 yrs.
Hellebores - if your soil is nicely mulched and organic to start with they reseed with a vengeance. I have hundreds of seedlings this yr to replant into the woods.
lily of the valley - takes anything you throw at it. Will be more dense if more moisture but weeds don't grow in it because the roots are interconnected and kind of webby.
Astilbe pumila Chinensis
Lady fern - a beautiful groundcover even for dry areas
Sensitive Fern
Christmas fern - an evergreen
daylilies - use dwarfs
Pulmonaria - one of my favorites - no weeds will grow in this once it gets going and it can take drought once established
Filipendula ulmaria Aurea - bright yellow foliage
Hardy geraniums - the pale pinks require less light
Brunnera
Comfrey
Sweet Woodruff
Tiarella's
Some various grasses - do a search
Carex species - can't be wet in winter so plant them in little mounds if your soil is heavy or wet
Oenothera - the yellow sundrops - watch out they reseed easily but can be pulled easy - are a pretty, clear yellow - can take high shade
Monarda Jacob Kline - I never would have known this could take so much shade except it seeded itself at the edge of the woods and does fine - more moisture makes it grow faster. - likes drainage. This is also true for Becky Daisy and Rudbeckia - Black eyed Susans. You'd be surprised how much shade they can take and still bloom heavily.

Other invasives are lirope and sometimes ajuga. I use ajuga all over my place and in some areas it spreads and others I have to keep replanting it - so depends on conditions. Liriope can be hard as heck to remove but its super effective as a dense groundcover if you can keep it in bounds. Less moisture slows it down.

Euonymous - I use a green and white variegated and also a green and yellow variegated that stay low to the ground. They will spread more in more light but they do offer nice evergreen foliage.

Vinca is a nice shiny green leaf with purple flowers in spring. The downside to vinca in my opinion is that it roots a little sparsely and can let weeds grow thru it. The upside to that is that you can interplant spring bulbs in it and they aren't choked out.

I let various columbines, Dames Rocket ( Hesperis matronalis) and a purple malva go to seed all over my shade gardens and then just remove what I didn't like after they bloom. They are all easy to pull with one hand.

Never under any circumstances except a buried 3 foot deep pot should you plant Houttuynia - chameleon plant, any mints, bamboos, chives, lemon balm, Chasmanthium - seeds heavily, Feasy grass and Campanula Cherry Bells. I have chocolate mint in a giant pot that I just keep at an edge because its fun to walk by and smell it - but would never plant it out unless it was bounded by cement.

Finally - the Lychnis family can be very very invasive and it runs very quickly - doubling and quadruping in size geometrically depending on how much moisture and light.
The plant called Gooseneck is an example. I planted it a wet area by the driveway because I don't think it can get away there - but if it starts to move into some other groundcovers I will use RoundUp on it - it has to be dug out with a shovel and fills right back in in a few weeks - thats how happy it is.

Come to think of it - watch all the Persicaria's also. I planted a cutting 4 yrs ago and it is all over my property now - it reseeds vigorously. I treat it as a weed now.