"Me and Bobby McGee" is Janis Joplin's most successful and recognizable song. Because she changed Bobby's gender from Kris Kristofferson's original version, she hints that she's singing from her own perspective and not that of a fictional narrator or protagonist.
When Joplin says "Me" in the song, listeners are sure that she is inserting her real self into the role of the narrating character and implying all of the notoriety, history, and attitude of her life along with it. The nameless narrator becomes a personification of a rock and roll icon who left the world too soon (Joplin's version of "Me and Bobby McGee" wasn't even released until after her death).
Though Janis Joplin changed the genders of the two characters, making Bobby McGee a he, she didn't have to change the much of lyrics thanks to Fred Foster, who is credited as a co-writer. Foster knew a female secretary named Bobby McKee, and he suggested that name to Kristofferson because it was ambiguous enough to fit either male or female (Kristofferson must have just heard, or wanted to hear, McGee instead of McKee; it's softer on the ears).
It was likely a business decision on his part, because he felt that this would allow for any singer to record the song, regardless of gender. This move paid off, as it led to Joplin being able to record the song to its pinnacle of success.