There is a young lady named Carol who hates Christmas. Partly it is because Christmas in Hong Kong is a meaningless shopping holiday, with no local religious, historical or cultural meaning. Mostly she hates Christmas because people keep making stupid Christmas-carol jokes about her name. The jokes are stupid, because the name Carol and the word carol, meaning a kind of song, are completely, wholly and totally unrelated.
The name Carol comes from the German and Old English name Karl. The original Old English spelling was ceorl and the meaning was man or husband. Today, English includes the word churl, meaning a common man, who is not sophisticated, gentle or upper-class. There is also the word housecarl, meaning a soldier who protects the home and family of a king or lord, especially in the days of the early English and related Germanic peoples.
There are versions of the name Karl in many languages. From the Czech we have král, from French we have the name Charles (and the women's name Caroline and Carol), Hungarian (Magyar) király, Latin Carolus, Russian король (korol) and Turkish kral. (Apologies for my pronunciation.)
The song carol means a joyful song, from about the year 1300 and from the Old French word carole. The original meaning was a kind of dance where the people dance around in a ring. (Scholars are not sure, but it might be from the Medieval Latin choraula, meaning a dance to the flute.)
People singing carols would gather outside the house of a very rich person and demand food and drink. Specifically they wanted a treat, such as Christmas pudding. The tradition is similar to giving red packets at Chinese New Year. A gift is provided in exchange for good wishes. (A Christmas Song Explained) Nowadays it's common in the UK to sing carols in the town square or going door-to-door hoping for contributions for a church or local charity.
The name Carol and the song carol have the same spelling, although the former is capitalised. Other than that they are completely unrelated. The name Carol comes from German and the song carol from French. The name Carol originally meant a person that might hit you very hard with a sharp spear and the song originally meant a silly dancing party.