Okay, so, I unticked the "Add speaker name" box from the Standard UI subtitle Panel, and then, in the Dialogue Actor component (see pic below), I ticked the "Set Subtitle Color" and "Apply color to Prepended name" boxes, turned the text black, and ta-da, it's working
I'm still unsure if there's a different box to prepend the actor's name, which I have ticked somewhere by accident, or does the "Apply color to the prepended name" box in the dialogue actor also prepend the name? I hope this made sense to you 'cause it almost didn't make sense to me...
Anyway, your advice got me looking from the right place and it's working now. Thank you very much once again!