Burbank is a unincorporated community in Santa Clara County, California. As an urban Island, it is surrounded by the city of San Jose. The population was 4,926 at the 2010 census. For statistical purposes, the United States Census Bureau has defined Burbank as a census-designated place. The area was named for horticulturist Luther Burba…Burbank is a unincorporated community in Santa Clara County, California. As an urban Island, it is surrounded by the city of San Jose. The population was 4,926 at the 2010 census. For statistical purposes, the United States Census Bureau has defined Burbank as a census-designated place. The area was named for horticulturist Luther Burbank.