Here is one splitting of the USA into four portions with approximately the same number of USAMO qualifiers in each.
Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey (65)
Pennsylvania, Delaware, Maryland, District of Columbia, West Virginia, Virginia, North Carolina, South Carolina, Georgia, Florida, Alabama, Mississippi, Tennessee, Kentucky, Ohio, Michigan, Indiana (62)
Illinois, Wisconsin, Minnesota, Iowa, Missouri, Arkansas, Louisiana, Texas, Oklahoma, Kansas, Nebraska, South Dakota, North Dakota, Montana, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada, Idaho, Oregon, Washington, Alaska, Hawaii (60)
Last names with multiple representatives:
ERRATUM: Xia actually had 1. Thanks to totalepicfailure for the correction.