This kind of piece is really a theme and variations. Another common type of piece is the Prelude and Fugue, two movements. The first is free-form, often melodic like a short sonata, or constructed of chords; the second is made like a round, like Row, Row, Row Your Boat except WAY more complicated.
Borne [borne] as a boys' name has its root in Middle English, and Borne means stream. Borne is an alternate form of Bourne (Middle English): place name.
Born and borne are alternate spellings of the same word, which is the past participle form of the verb bear. Even though, as verbs, they function the same in a sentence, they are used in different contexts.