In Chinese, Sodium is "鈉" (Nà). Is this because it's also the elemental symbol?

I have heard that, since there were no characters in traditional Chinese for most of the chemical elements, the modern names were chosen based a a number of criteria, including whether a traditional word exists, and if not what the common accepted chemical name, or even part of the English name, etc. I think, in the case of sodium, it is from the Greek word ‘natrium’ which is where the symbol Na comes from.

More info can be found here: https://en.wikipedia.org/wiki/Chemical_elements_in_East_Asian_languages

And here: https://languagelog.ldc.upenn.edu/nll/?p=18877

Edit: FWIW, the Japanese version of Tom Lehrer's song is cute