Russian Meaning: The name Karol is a Russian baby name. In Russian the meaning of the name Karol is: Strong. Slavic Meaning: The name Karol is a Slavic baby name.In Slavic the meaning of the name Karol is: Manly. SoulUrge Number: 7. Expression Number: 3. People with this name have a deep inner need for quiet, and a desire to understand and analyze the world they live in, and to learn the deeper truths.he name Karol is a Russian baby name. In Russian the meaning of the name Karol is: Strong. Slavic Meaning: The name Karol is a Slavic baby name.