The repetition of the same word or phrase at the beginning of successive clauses or sentences is called anaphora.
The term comes from the Greek word anaphora, meaning “carrying back.” In rhetoric, anaphora deliberately places matching language at the start of neighboring clauses to create emphasis, rhythm, emotional force, or memorability. For example: “We will work, we will learn, we will improve.”
A famous example appears in Martin Luther King Jr.’s “I Have a Dream” speech, delivered in 1963, where the phrase “I have a dream” returns at the beginning of successive statements. Winston Churchill’s “We shall fight...” passages also demonstrate the device.
Anaphora is often confused with epistrophe, which repeats words at the ends of successive clauses. When a passage uses repetition at both the beginnings and ends, the combined device is called symploce. Chiasmus instead reverses the order of words or ideas, antithesis contrasts opposing ideas, and litotes makes an understatement through negation. In linguistics, “anaphora” can also describe a reference to an earlier expression, but in this question the rhetorical meaning is the clear canonical answer.