If someone transitions from male to female (or vice versa), and they're becoming a new person with a new identity, do they retain the same
birth/astrological information?
After all, they're creating a whole new persona.
If it is a form of rebirth, what is the best way to determine the new birth information?
The basic natal chart is the same. The idea is that, they were always who they were, they just hadn't expressed it to the world before.
However, it would be interesting to look at the chart of their "debut" to the world as the new gender. I just don't think you can pinpoint one instance that describes it. It could be the moment they make a commitment to transition, or their first public appearance (which gets into the question of whether someone they know well counts, or it has to be strangers in the general public), or the moment their new look is first put together or they decide on a name. Don't think there's an official answer on this, maybe it's up to the individual.
I definitely think the natal chart is still relevant even after transitioning. Our sex is only one aspect of our being. Everything changes all the time.
I don't think theirs will be a new birth chart altogether.
Transits in their birth chart will show a triggered interest in identity-alteration.
Also natal planets in their birth chart could reveal that at some point in their lives they'd want a change in their identity; or could be conflicted within themselves; or a lack of understanding of their identity (Moon and Sun issues).
Also, the chart of the surgery could be drawn up - to understand how the outcome of the surgery would be, and when surgery related issues could crop up.