Rockets have technically been around since the Chinese invented gunpowder (from saltpeter, sulfur, and charcoal dust) but I don't think they bothered to name them. The Chinese used these rockets both for warfare and celebrations (i.e. fireworks shows).
The first rocket with the capability of reaching what we call space (60 ~ 70 miles up) was named Vergeltungswaffe 2.
In 1969, the first rocket went to the moon. The name of the rocket that propelled them into space was the Saturn V rocket.
The Explorer but it wasnt a rocket, it was a satellite
Eagle
Vostok 1
APOLLO 13
The name of the rocket that launched the first people on the moon was a Saturn V, on mission Apollo 11.
Saturn
we doubt, it is SLV 3
Apollo 11
The first rocket to reach space was the German V2 in the 1940s. The first spacecraft to achieve orbit was the Soviet Sputnik, launched in 1957.
There really isn't a name for his rocket, though it launched it on March 16, 1926 in Auburn, Mass.
Waiting for my Rocket to Come