Coca-Cola trademarked the brand name “Coke” in 1945. Although consumers had used the nickname for years, the company did not immediately treat it as the drink's official name. Coca-Cola formally adopted the nickname in 1941 and then registered it as a trademark four years later.
The distinction between 1941 and 1945 explains why this question can cause confusion. 1941 marks the first official use of “Coke” as a Coca-Cola trademark in advertising, including messages explaining that “Coke means Coca-Cola.” The legal registration followed in 1945.
The company had practical reasons to protect the nickname. It feared that another business might claim the name, and it also worried that “coke” could become a generic term for cola drinks. In parts of the southern United States, people have sometimes used “coke” to refer to soft drinks generally, but that regional usage does not change the trademark's registration date.
Coca-Cola itself had been trademarked decades earlier. Asa Candler applied for that brand's trademark in 1892, shortly after the Coca-Cola Company was organized.