Alpha particles were first described in the investigations of radioactivity by Ernest Rutherford in 1899
I can't access the paper containing this discovery (because it is still behind a paywall 120 years after it was first published). Perhaps Rutherford et al. didn't yet know what they were looking at so just called it "alpha" radiation? Only later did we understand this was due to a helium nucleus?
Another related question is why do proton and neutron radiation not get special names, where they not as easy to observe by the zinc sulfide detection method that gave off a flash of light, or by cloud chambers?