甲方:[name] 乙方:[name]
甲方 / 乙方 + 应 / 应当 / 有权 + [verb phrase]
甲乙双方 + [verb phrase]
甲方 and 乙方 are how a contract refers to its two parties. 甲 and 乙 are the first two of a traditional series used for ordering, like A and B, and 方 means "side". The contract names each party once at the top and from then on uses only the label.
甲方 is usually the side that commissions the work or pays, and 乙方 the side that provides it. A third party is 丙方.
甲乙双方 or just 双方 covers both at once, typically in the clauses on signing, changes and disputes.
Once the parties are labelled, the body never switches back to names or pronouns, and the labels aren't translated from English numbering.
In office talk, 甲方 also means "the client" in general – the side that sets the requirements – and 乙方 the supplier who has to meet them.