You can choose Riverrun Minstrel as the target of it's own ability because she is already in play when her reaction triggers. This is similar to marshalling Melisandre and then triggering her reaction because Melisandre, a R'hllor character herself, entered play.
- When a card's ability text refers to its own title, it is referring to itself only, and not to other copies (by title) of the card. RRG page 19. This means that when you bring Minstrel #1 into play, you CANNOT also trigger Minstrel #2 that you already had in play.