According to the Star Wars: Blueprints - Rebel Edition factbook, the Tantive IV was renamed in honour of representatives from the distant Tantive system.
The Corellian Engineering Corvette CR90 is the starship of choice for
everyone from respectable diplomats to notorious pirates. More than a
decade before the Clone Wars, Queen Mazicia Organa of the planet
Alderaan commissioned the Star of Alderaan to serve as a consular
vessel for Senator Agrippa Aldrete. After the queen's son, Bail
Organa, ascended to Viceroy and became a Senatorial representative, he
renamed the ship the Tantive IV in tribute to visiting ambassadors
from the Tantive system. It served House Organa for 30 years until its
capture by the Empire, after which Darth Vader ordered it be
Star Wars: Blueprints - Rebel Edition
Star Wars Insider Magazine identifies the fourth planet of the Tantive System as having engaged in an exchange of arts and artists with Alderaan prior to the renaming of the ship.
The fourth planet in the Tantive system is home to the Tantive Gallery
of Progressive Arts, a sister gallery to Alderaan's own Aldera Museum
of Modern Expression. A cultural exchange program of art and artists
preceded the naming of the starship.
Star Wars Insider #90
Image Courtesy of The Official Star Wars Fact File #11 - "Tantive IV: Blockage Runner"
Out of Universe
The ship's name wasn't included in the original script or film novelisation.
The ship was merely referred to as a "blockade runner".
The awesome yellow planet of Tatooine emerges from a total eclipse,
her two moons glowing against the darkness. A tiny silver spacecraft,
a Rebel Blockade Runner firing lasers from the back of the ship, races
Star Wars: A New Hope - Final Draft Script
The name 'Tantive IV' was subsequently added by Brian Daley for the (NPR) Star Wars Radio Play. According to Lucasfilm's Pablo Hidalgo (in Star Wars Insider #90), the name was based on the obscure English word "Tantivy" meaning 'to gallop at full speed'