Phoenix takes its name from the mythical bird said to rise renewed from its own ashes, and the name is used almost entirely for that association with rebirth. It suggests resilience specifically tied to recovery -- not simply enduring hardship, but returning changed by it.
When the significator of either good or evil shall be stationary, and angular, it shall be more durable. But it shall be the more mutable and variable, if the significator shall be cadent from angles, and retrograde. - William Lilly (1602.-1681.)