I cut a dried out, seemingly dead olive tree to the stem last year. Over the last six or so weeks there's been new growth out of the stem. But is this an olive tree? The leaves don't look quite like an olive tree's leaves.
If the stump is the stump of an olive tree, then those are olive leaves.
It's quite common that regrowth from a stump, after the main tree is cut down, will look a bit different from the original leaves. The tree has lost its entire source of food, and is now down to just what it has stored in its roots. So it's frantically trying to grow new leaves, as quickly as possible, in order to start bringing in some food. So it prioritizes leaf surface area over defenses, like waxy coatings or hairs, that it would normally use to protect its leaves from herbivores, water loss, and sunburn.
If they survive, those fresh, bright green leaves will eventually develop the normal silvery sheen that olive leaves have. In the meantime they will be particularly attractive to herbivores, so protect them from deer, rabbits, goats, etc. if you want to give your olive tree the best chance to grow back.
Sometimes regrowth from the stump of a cultivated tree will actually be a different variety or species, although closely related to the original tree. That's because many cultivated trees are created by grafting a stem from one species or variety to the roots of another species or variety. That allows us to get beneficial traits from two different plants. Usually the root stock comes from a plant with particularly hardy or disease-resistant roots, and the top comes from a plant with attractive foliage, a sturdy trunk and branches, or delicious fruit. When you have a grafted plant, you'll usually be able to see a bump in the stem where the two different plants were joined. If your plant had a graft, that bump would have been above the cut, and this new growth would be from the rootstock. So, it might be the case that any olives that eventually grow from this rootstock won't be very good to eat.