Well, the name was already taken.
Genealogy is the study of family origins. It is how people trace their ancestry and create a family tree. It's not a biological science. Genealogy has been around for a long, long, time before we discovered genes.
The science of genetics began in the 1800s when Gregor Mendel figured out how traits are inherited by studying peas. Since scientists identified genes in the mid-1900s, the field of genetics has grown by leaps and bounds.