What are the radical names? I noticed the kangxi radicals all have two ways that people refer to them.
For example: 氵 is sometimes called shuǐ, sometimes called 三点水. 饣 is sometimes called shí or 食字旁.

What are the correct names for the radicals as radicals?

there's lots of these on Wikibooks and in the other way at archchinese.com.
In my opinion, 三点水 and shui3 are all correct names for 氵, so for 饣.

Actually, 氵is also 水, just in another face. 
You can know this by comparing Chinese Seal Character(小篆)
河:http://www.zdic.net/z/1c/zy/6CB3.htm
水:http://www.zdic.net/z/1c/zy/6C34.htm

三点水 is more formal, shui3 is most used in computer world.

Hope my explanation can help you understand this further.