ST. LOUIS — On July 3, one of this country’s most recognizable landmarks will be reintroduced to the world with a new name, a new museum and a substantial redesign of its urban landscape. A half-century after Eero Saarinen’s Gateway Arch was inaugurated in 1968, it has been reconnected to the city of St. Louis, with a sleek underground entrance facing the city, an expanded and redesigned visitor center and museum, a cleaner landscape and an elevated and more elegant waterfront along the Mississippi River. An old parking garage has been removed and a parklike pedestrian platform over Interstate 44 allows visitors from downtown St. Louis to visit the city’s most popular attraction without having to brave traffic lanes.