Why is it called specific gravity, when it defines the ratio of densities?

The correct (and more meaningful) term is relative density.

It measures the ratio of two densities, where one is a reference one (usually water). So the specific gravity (SG) of a substance $x$ with respect to water is $$SG=rho_x / rho_{water}$$

Why specific?

Specific means "per unit volume". Because the mass of an object is given by

$$M_x=rho_x V_x$$ if you take the same volume $V$ of the substance $x$ and of water and you weight (measure the mass) the ratio is going to be

$$M_x/M_{water}= rho_x V / rho_{water} V= rho_x / rho_{water}$$

Usually specific means that the quantity does not depend on how much you consider, if you take 1 L of ethanol or 2 liters - they have the same SG because you need to compare it with the same amont of water and the volume goes away in the ratio.

Why gravity

Because, as you saw before, it is related to mass i.e. to gravity in a way (when you measure a mass on a scale you are actually measuring its gravitational force). To measure the SG you need to either weigh a fixed volume of of $x$ and compare its weight to the same amount of your reference substance (water in our case) as we did before. But you can also find the volume $V_x$ at which the weight of $x$ equals a given volume of (e.g.) water.

Indeed, you can measure it by putting the two amounts on a scale (the one with a lever and two things to be weighted at the same tme, old style) and see when the scale measures the same mass. When that happens, because you now know the volume at which the masses equal each other you can write $$M_x=M_{water}$$ which means $$rho_xV_x =rho_{w}V_{w}$$ i.e. $$SG=rho_x/ rho_w=V_w/V_x$$ so you can extract the specific gravity by measuring things on a scale i.e. weighing them i.e. using gravity.

(Of course, as we said before, you can choose any reference volume of water: this will result in a different volume of $x$ but the ratio will be independent of the volume)

Other options are: immerse your substance in water and see if it sinks. Or use one of the many instruments described on wikipedia (: most of them however relate on gravity as a way of measuring the SG.