What was the name of Alexander's half-brother who succeeded him as king?

Alexander's half-brother Philip III, born Arrhidaeus, succeeded him as king of Macedon after Alexander's death in 323 BC.

Alexander died in Babylon without an adult legitimate heir. His wife Roxana was pregnant, but the child’s sex was not yet known, creating an immediate succession crisis among the Macedonian army. The infantry supported Arrhidaeus, while Perdiccas and other commanders wanted to wait for Roxana's child to be born.

A compromise made Arrhidaeus king under the name Philip III. When Roxana gave birth to a son, the child became Alexander IV, and the two were recognised as co-kings. In practice, neither ruled independently: powerful generals such as Perdiccas and later Antipater acted as regents and controlled the empire.

Philip III was therefore Alexander's first successor in the formal monarchy, but he was not the only royal successor. Alexander IV was his posthumous son and co-ruler. This is why questions that say simply “who succeeded Alexander?” can sometimes produce confusion, although Philip III is the canonical answer when asking specifically about Alexander's half-brother.