Like most other Nanoha characters, she is named after a car. In her case, the Subaru Vivio.
In ViVid, she is referred to as Takamachi Vivio (ι«ηΊ γ΄γ£γ΄γ£γͺ), having been adopted by Takamachi Nanoha at the end of StrikerS. She was cloned from the Saint King Olivie Segbrecht.