How should I avoid being in the shadow of my PhD advisor after I have my own faculty position?

I find a little radical to stop collaborating scientifically with her (in part because there is no one around working on this area!), but as the time goes by it seems to me that the best option is to start working alone on this common area, or some similar solution...

There is some truth to the often-heard advise that one should stop regularly collaborating with one's PhD advisor after getting a PhD. I would argue this is doubly the case when you and your advisor work at the same place. To the outside world, you will always appear to be the "junior" in your collaboration, independently of who does how much work, who has had which ideas, or who is where in the paper author list.

My impression is that in the career stage that you are in, you should prioritize collaborations where you are the most senior person in the team, or where you are at least not overshadowed by somebody much more famous than you. Work on papers with your students, or with other people in a similar or earlier career stage than you. Avoid collaborations where you do all the work and some other eminent figure in the community (your advisor or some other senior professor) could be seen as the strategic brains behind the work.

Here is a somewhat radical suggestion that my apply or not, depending on personalities. If your mentor/collaborator is anywhere near retirement this may be especially useful. It is a bit risky (or not) depending on her attitudes and place in the profession.

But you could, perhaps, just start a conversation with her letting her know that you think your career "needs a boost" and ask if she can help you get to the next level. Many people will respond positively to this, in fact. My personal attitude is that I am happiest when I fall into the shadow of one of my former students. After all, our job is to advance the state of the art, not only through our own work, but by teaching students to do the same.

If she thinks enough of you and of the work you both are doing, she will want it to continue after she leaves the scene and you are probably a good vehicle for carrying it forward.

But small steps are to make sure that you go to those conferences with her and become personally known in the community. Find a way to be the presenter of your joint work. Find a way to be the corresponding author on papers so you get contacted by committee chairs and editors.

Don't ignore the other answers here, of course. Work that you do alone or with other collaborators will help distinguish you from your former advisor. But it is a long process. Your early-career tag on the question says a lot. With ten years in the saddle you have a long way to ride and your former advisor won't be a riding companion for the whole way. But take advantage of your association while you can, rather than trying to sever it. Make her the champion of your career advancement if at all possible.

I believe the infallible way towards academic recognition is being clearly responsible for major breakthroughs in your field. Probably you have put yourself where you are, by consistently directing the spotlights to your senior author(s). Making someone else honorary first/corresponding author, as well as letting them present your work sure "gives face" to peers and shows reverence. If you got where you are because of such acts of "loyalty" then stopping it will quickly generate conflicts. But unfortunately there's no other way around this: publish independent research (meaning the best you can produce), stand where you belong, present your work directly. No more special thanks at the end to honorary seniors. Discuss that openly with your ex-advisor, who may feel betrayed.

And by all means, do not expect nor induce some student to give you the face you've given your advisor as in the shape of some karmic payback. This is not a cycle.