The wanted meanung was "The Rock" (The one and only).

Alterum - The one
Saxum - Rock

As it seems a clear translation of the wanted "The (one and only) Rock" is not possible.
Another try was "Saxum Saxorum". This means "The Rock of Rocks" which would be a little more clear, but as "Alterum Saxum" sounds better "Alterum Saxum" was born.