It's an odd little reverse of the expected that sodium is actually derived from soda, which was a fifteenth century term for a mysterious alkaline substance. Sodium, was not isolated and named until 1807. Soda itself probably comes from the Arabic suwwad, which is the name of a sort of herb.
The chap who invented, or discovered, sodium, was Sir Humphry Davy, who has great literary significance as he was the subject of the first ever Clerihew, an odd sort of four-line poem that has a man's name as a first line.
Sir Humphry Davy
He lived in the odium
Of having discovered sodium.
He was also the first Englishman to use the word potassium, which is named after potash.
Soda water is first recorded in 1802 as a name for fizzy water with bicarbonate of soda in it. To an Englishman, soda remains just the name for carbonated water, however in America it is a generic name for fizzy drinks. This map shows the Arab word's infiltration of the United States (double click to enlarge):