This eponymous orchestra had its roots in a salon ensemble created by Nathaniel Shilkret, music director of the Victor Talking Machine Company between 1916 and 1935. Based in Camden, NJ, across the river from Philadelphia, Victor (which merged with RCA) was able to use players from Leopold Stokowski's orchestra on an ad hoc basis as late as 1940. By then it was called the "RCA Victor Orchestra" -- not, however, to be confused with another ad hoc group, called simply the Victor Orchestra, in NYC for lighter music on the company's budget-black and blue labels.
The merger with RCA, the Great Depression, union-czar's James Petrillo's ban on stateside recording in the early 1940s, and the Philadelphia Orchestra's defection in 1943 to Columbia Records (a CBS affiliate) changed the playing field. New alliances between overseas and USA labels complicated matters after World War II, exacerbated by Columbia's acquisition of the Metropolitan Opera, many of whose singers were already RCA artists. The "RCA Victor Symphony" suddenly became a major player, based chiefly but not solely in Manhattan, which boasted a vast reservoir of players.
The RCA SO wasn't, however, just an operatic project. Leonard Bernstein made his first records with it as a Victor artist (1944-1950). Igor Stravinsky, based in Hollywood, also conducted RCA SO records, both there and in Mexico City. Jascha Heifetz recorded several concertos with conductors William Steinberg and Izler Solomon. All of Robert Shaw's RCA recordings drew from the New York pool. However, the principal conductor of RCA's complete operas in a war with Columbia was Renato Cellini, until Fritz Reiner left Columbia for RCA in 1950.
Victor's NYC players came from the Philharmonic, the Met, the City Center and NBC Orchestras and radio staff musicians. When Fritz Reiner entered the picture, contractors of his choosing engaged the requisite number of players -- thereby guaranteeing performance consistency -- whether in J.S. Bach's Brandenburg Concertos, Strauss' tone poems, concerto accompaniments, or opera excerpts (with several of the Met's leading singers in then-current productions of Die Fledermaus and Der Rosenkavalier, plus a complete Carmen). But while Fritz Reiner may have been primus inter pares, others recorded with the "RCA SO" including Leopold Stokowski, Krips, Kondrashin, and Alfred Wallenstein. Los Angeles was the second center for eponymous recording orchestras -- there were Columbia and MGM symphony orchestras as well as the one at RCA. The area had a pool of first-class studio players and Philharmonic personnel (who anchored most of Bruno Walter's last hurrahs, and whatever I. Stravinsky did not record in Toronto or New York).
Until the simultaneous advent of stereo and year-round contracts, major USA symphony orchestras played summer concerts. Thus, Everest could record the NY Phil as the Stadium SO; RCA could record Philadelphia as the Robin Hood Dell SO, and the LA Phil as the Hollywood Bowl SO. But those were aliases, not commercial eponyms.
However, when film production headed overseas in the 1960's to economize, so did RCA, whose USA Symphony Orchestra was replaced by an RCA Italiana Orchestra, off-season Rome Opera players recruited for operas by Verdi, Puccini, et al. In 1963, after Chicago, Fritz Reiner recorded Haydn symphonies in NYC with "his orchestra" (a Leopold Stokowski nom du disque dating back to the 1940s). Although USA record companies retained "name" orchestras to challenge a flood-tide of product from Europe, classical music sales dried-up in the 1990s like the Serengeti. Bertelsmann, a German media conglomerate, bought RCA Red Seal Records but put its century-old backlog to the sword in 2001, so that the last published issue of Schwann Artists had no listing of the RCA Victor SO per se.