when people say "clinton" i think of bill, this is probably the reason the campaign is using "hillary" so much. it's not about gender, it's about distinguishing one person from another. you could say "hillary clinton" every time, but what to use when using just one name? back to "hillary."
of course, the reason that i associate "clinton" with "bill" is that i have forgotten what life was like during the clinton administration. i certainly don't like the person we have now, but i didn't like bill either- and as many people did at the time, when people said "bill clinton" i thought: "hillary."
either way, she's better off NOT using "clinton" these days. "hillary" almost sounds like "a different person," which is exactly what this country needs.
i'm not that optimistic. i'm pretty tired of the junta that's been running the country into the ground for the past 20 years straight- bush, other bush, clinton, and (my guess) other clinton. will hillary's administration be much different than bush's or her husband's was? anything she can do to convince people it will be can only help her campaign.
as for gender, she can and most likely will play to the idea that being a woman will automatically make her a more humanitarian leader. tell that to margaret thatcher- though i would be very happy to see any woman in office, provided that i had any reason to think her policies would be humanitarian.
I think it is part of the marketing. She is the only female in the race. Using her first name is going to make her stand out.