It's a submarine-launched ballistic missile system comprised of the Trident missile, the special Trident warheads and the Ohio-class ballistic missile sub.

The US Navy currently has 14 active duty Trident (Ohio Class) Ballistic Missile Submarines. They are scheduled for replacement beginning in 2028.

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Actually, Trident and Poseidon are the names of the missiles... various types of submarines can carry these types of missiles.

Poseidon is an older missile system. Polaris is also an older type of missile system. Polaris succeeded Poseidon, and Trident succeeded Polaris.

It does not have a known name apart from 'trident'.