I was given one (no name) that looks much like the white garlic chive you picture. It is a very pretty fall blooming onion and bees love it. As it springs up all over the yard, it is very pretty in the fall when there are few white flowers. BUT: It self seeds like crazy. The bulbs multiply into tight clumps. The only way to eliminate them is hand digging and that is difficult in and around other plants. They are almost impossible to pull and can not be killed with weed killer. I've also found if I pull without gloves the oil stings. If the clumps are allowed to continue, eventually they push and eliminate other plants. When they come up in my brick walk, they actually push the bricks aside. Unlike many well behaved examples, this one is less a blessing in Zone 4-5.
Wow...the only 'invasive' onion I have is Allium cyathophorum var. farreri..it self-seeds and pops up here and there but the bulbs are not deep so it is easily removed. My garlic chives have NEVER self-seeded..it blooms too late here to ever set seed.