I suspect that one of my past-life names was Jane Grey.
It's not exactly that I "remember" it. All my life, the name Jane has "struck" me --- not necessarily attraction or repulsion, but evoking intense and indescribable emotions.
I wrote a novel in which the main character is a precocious heiress who publishes a story under the pen-name Jane Grey. After I finished the novel, I googled all the character-names in it (curiosity --- and concern over whether a real person would sue me
).
I discovered that Jane Grey was a minor British historical figure --- a queen of England for nine days, who was executed at the age of 16.
There are odd parallels between the story of Jane Grey and my novel:
My main character, Constance Fairchild, is very precocious at a young age. As a teenager, Jane Grey was one of the leading minds of 16th century Europe.
My character travels to Switzerland and Germany. Jane Grey corresponded with intellectuals in those regions (I imagined she always wanted to travel there).
Jane Grey was an early protestant and was executed at the order of the catholic Queen Mary. (Her religion was one reason she was placed on the throne). In an early version of my novel, Constance Fairchild gets into a shouting match with a catholic priest (for no apparent reason --- it's hate at first sight).
Jane Grey was executed at the age of 16 (for usurping the normal law of succession, even though others forced her to do it). Constance Fairchild is almost murdered at that age by people trying to seize her family's fortune. She escapes by a clever ruse.
Jane's parents were very extremely abusive (even by the standards of 16th century England). Constance's are distant and die early on in the novel.
The accounts of Jane's life seemed oddly familiar to me when I read them. And, in many ways, the novel is like a "new and improved" version of Jane's life.
The novel itself came to me in two concurrent dreams (!?) in which I was female. These were "epic" dreams in which years seem to pass (I've had four or five such dreams in my life).
The two dreams paralleled each other. One took place in 16th century England and its major events followed what is documented as Jane Grey's life (although I wasn't conscious of having that name in the dream --- I was very aware that it was the 16th century and England). The dream had other events, too, that don't contradict anything known about Jane Grey's life.
The other dream was set in the near, but indefinite future and formed the novel. I wasn't conscious of "my name" in that either, but picked the name Constance Fairchild for the novel's main character. (I had an aunt named Constance, in my "current life").
If you feel no strong pull towards the name either way, maybe you should just write it down and put it aside until more information comes to you. 
