Roman Catholic is a perfectly acceptable name for the local Catholic Church, however “Latin rite” is not the name of the church, but only the rite used. For instance, Saint Mary in Colchester, identifies itself as a “Ukrainian Catholic” parish, not a “Byzantine rite” parish on its front sign. The Cathedral of Saint Joseph likewise identifies itself as “Roman Catholic” rather than “Latin-rite”.
It uses “Roman Catholic” to distinguish itself from all other “Catholic” churches, such as the Polish National Catholic Church, which have a presence within the boundaries of the diocese. The term “Latin-rite” does not offer this distinguishment, as the Polish National parishes also follow the Latin-rite, as are several Eastern Orthodox parish that use the Latin-rite. Eastern-rite parishes similarly use the name of their church to distinguish them from Eastern Orthodox parishes.
Also relevant, Connecticut state law sets up a special kind of corporation for the Catholic Church, where all parish property is held in trust by the bishop, but each parish has its own legal personality, reflecting internal church law. The state law uses the term “Roman Catholic”, thus the diocese uses the legal name “Hartford Roman Catholic Archdiocesan Corporation”, whose sole trustee is Archbishop Mansell.