A. History of naming formula
Naming formula or the language of chemistry was largely based on the work of Antoine Lavoisier (Father of Modern Chemistry). He worked to translate the archaic and technical language of chemistry (about 19 century). Then the names of formula was developed by a group of scientists. Elements are represented by symbols. Each formula has a name unique to that formula.
B. What is the concept behind the naming?
In the past, the chemists used formula or elements by drawing or using shape to describe the formula. But it very hard to understand so that naming the formula made it easier to understand and to use at more interesting for people to learn. Naming the formula allows chemists and people to communicate in words rather than in chemical symbols.
C. Does "ate" represent 3 Oxygen atoms?
No, it doesn't. There are many formula that have "ate" but more than 3 oxygen. Example: PO4 (phosphate), SO4 (sulfate)
References:
http://www.miracosta.edu/home/dlr/naming.htm
http://en.wikipedia.org/wiki/Chemical_formula
http://en.wikipedia.org/wiki/History_of_chemistry
http://en.wikipedia.org/wiki/Chemistry
