Please don't type in all caps. It is against the rules of this board, and many people consider it to be a rude form of "shouting" on the Internet.
Riquette is probably just a feminine form of
Richard created in the USA and given a "Frenchified" spelling. However, Riquet is a French surname which goes back to a medieval male pet form of either
Richard or
Henry in
France, so it is just barely possible that Riquette could be considered the feminine form of Riquet. In that case it is based on the syllable
ric which was common in Germanic names.
Ric originally meant "power."