The internationally agreed symbol for 10^6 is M and this is the initial letter of million. Would it not be logical and convenient to turn this happy accident into a principle and use G, the internationally agreed symbol for 10^9, as the initial letter of the word for 1,000,000,000? That number would thus be called a gillion. Whether the g should be hard or soft is a matter of opinion. I incline to hard because of the derivation from giga.
Source: wiktionary