In 1849, the island is still swedish. I don't know if it's like in Guadeloupe where the lack of family names indicates that the people concerned are freed slaves or free people of color.
After the end of slavery in 1848, the French authorities gave surnames to all the newly freed slaves. Slaves only got a first name. It took several years. For example, on the small island of La Désirade in 1849, most of the grooms and brides only have given names because they haven't been registered yet.
The people freed between 1837 and 1848 received a family name during the manumission process.