I can't tell you what kind of plant you have, but I can tell you that the white things are mealy bugs. The second picture you posted shows both the adult mealy bugs and the young Nymphs (also called crawlers).
Mealy bugs are a type of soft scale insects. They feed by sucking the juice from plant leaves and stems.
I have dealt with mealy bugs a lot on Marantas (Prayer plants, Calathea, Stomanthe, etc ...). They love to hide in the leaf sleeves that Prayer Plants have. A trick that I used to find them was putting a bright light behind each stem. The mealy bugs hiding in the leaf sleeves showed up quite well. Although that won't work with the plant in the picture, it is something that you can maybe use to check for mealy bugs on other plants you might have.
Getting rid of mealy bugs is a bit tricky because they will often hide in any crevice on or near the plant. That includes the outside of the planter the plant is in and the surface the planter is sitting on (such as window sill or a plant stand).
Adult mealy bugs will cover themselves with a white waxy coating that protects them from a lot of insecticides. So the best to get rid of mealy bugs is a 3 step process . . .
Step 1 ~ Use Q-tips dipped in rubbing alcohol to remove all the adult mealy bugs you can find. Don't forget to check all folds and crevices in the stems and leaves.
Step 2 ~ Mix a few drops of Dawn dish liquid, about 3-4 tablespoons of rubbing alcohol with distilled water in a spray bottle. Spray the plant thoroughly, making sure to get all stems and leaves.
Step 3 ~ With a paper towel (or a cloth rag) moistened with rubbing alcohol, clean the rim and outside of the planter (don't forget to clean under the rim. Mealy bugs love to hide there). Also use the alcohol to clean the surface around the planter.
You will need to repeat steps 2 and 3 (repeat step 1 for any adults you find) about every 3 days until there are no longer any signs of mealy bugs on the plant. This usually takes about 2 weeks, to be on the safe side.
Also, if you have other plants, don't forget to check them carefully to see if the mealy bugs have spread to your other plants.