The first one is a type of dracaena. I am not sure exactly which type.
The second one is called massangeana cane.
They require moderate light (not a lot) and they don't like water a lot. Even when the surface is dry, you don't need to water yet. I would say that once per week is a bit too much.
Also, they don't like flouride. So leave water sit in the room for 24-48 hours before watering the plants.
If you have had them for a few years, you should consider changing the soil. I actually do that every year. Get some potting soil and change all my plants every spring time. Then I leave them in the garden for a couple of months. They grow fast.