I have the same situation. I legally changed my name to my step-father's name, so that would be the Current Last Name, Birth Name is Last Name at Birth. When I married, that name goes into Other Last Names, but for a male, it would go in Current Last Name because that is what he goes by.
I have genealogy for my step-father, but my genealogy line follows the Birth Name, not the step-parent. You stated he wasn't adopted, so that isn't a problem. Your mother will have 2 husbands, so you can follow and add to your step-father's genealogy, also, if you want to.