I'm planning a project requiring a rotating table.
The problem is, I don't know the proper name for the bearing used on the rotation axis.

I know that regular bearings (e.g. roller-blades) won't do because they are not designed to carry a load on the rotation axis.
The closest common application (I can think of) for the bearing I'm looking for is for a roulette wheel.

Could the term be "Thrust bearing" ?

As used in a washing machine?

Tapered bearing. Like those used on the spindles of cars and trucks. If you go to a place that sells bearings and tell them what you want they should be able to advise and give prices.

angular contact bearing?

Thrust Bearing is the correct term.
They come in many diff. configurations, including tapered and angular styles.
A spinning bearing has loads is a radial direction and axial direction. When designing, you need to consider the amount of force/load the bearing will have to handle in both directions. Because everyones application is so different, there is no black or white awnser, just varying shades of grey, so to speak. Heavy thrusts @ low speeds may be better suited for a tapered bearing, if the thrust is not severe, you may be able to stack angular contact bearings in the correct order, to achieve support, You may also be able to use a "Conrad" style radial bearing with deepgrooves. There is a trade off for each, speeds they can rotate at, the amount of "room" they take up in your assembly ect....

hope this helps

Heavy thrusts @ low speeds may be better suited for a tapered bearing

Thanks, now I know what to look for.
My application will probably not strain the bearing too much.
I'm looking at a weight of about 4-6 lbs, and very low speed of about 20 rpm.

How big of one do you need? I have a few NTN 16026 deep groove radial bearings floating around here.
O.D.- 200 mm
I.D.- 130mm
THK- 22 mm
Load- 17,900 lbs
They were used in panoramic x-ray machines, head rotation assy's. Those x-ray machines at the dentists office that go around your head. At one time I was going to make a rotary table and then a large turntable for one of those garden railways, but never got around to it.

I was thinking about I.D. of 5/16", to fit my existing hardware.
17,900 lbs is 3 orders of magnitude more than I need.
I can probably manage with low end bearings.

Sounds like you can use rollerblade bearings.