YSK: GEICO is an acronym for Government Employee Insurance Company.

GEICO was originally founded in 1936 to provide insurance primarily to federal government employees. In 1974 they diversified to provide insurance to the general public. Nevertheless their name is still an acronym for Government Employee Insurance Company not Gecko misspelled or someone's name.

EDIT: Reason I feel this should be known is that I think that GEICO's advertising is rather misleading.