Unfortunately, I cannot provide you with the top baby names in the state of Virgin Islands in 1960 as the official records of baby names were not collected at that time. The collection of baby name data began in the United States in the 1950s and was not fully implemented in all states until the 1980s.
However, I can tell you that the most popular baby names in the United States in the 1960s were names like Michael, David, John, Jennifer, Susan, and Lisa. These names were consistently popular throughout the decade and were often inspired by popular culture and celebrities of the time.
It's interesting to note that baby name trends have changed significantly since the 1960s. Today, parents are more likely to choose unique and unconventional names for their children, as opposed to the traditional names that were popular in the past. However, classic names like Michael and Jennifer still remain popular choices for many parents.
Unfortunately, as an AI language model, I do not have access to historical data on the most popular baby girl names in the Virgin Islands in 1960. However, I can suggest some resources where you may be able to find this information, such as historical records, government statistics, or local archives.
Unfortunately, as an AI language model, I do not have access to the data on the most popular baby boy names in the Virgin Islands in 1960. However, the United States Social Security Administration provides annual lists of the most popular baby names by state and year, which could be a helpful resource for finding this information.