An earlier version of the script makes it pretty clear that a primary part of Leia's mission was to make contact with Obi Wan Kenobi and return with him to Alderaan.
PRINCESS LEIA :
General Obi-wan Kenobi, I present myself in the name of the royal
family of Alderaan, and the Alliance to restore the Republic I break
your solitude at the bidding of my father Bail Antillies, Viceroy and
Chairman of the Alderaan system. Years ago Commander you served the
Republic in the Clone Wars. Now he begs you to aid us again in our
most desperate hours. He would have you join him on our home planet
You must go to him! I regret I am unable to present my father's
request to you in person ... my mission to return with you has failed,
information vital to the survival of the Alliance has been placed in
this droid...my father will know how to retrieve it. I plead with you
to see this R-2 unit safely delivered to Alderaan. You must help me,
you are my last hope.
Since she apparently knows that he's not dead, and since she's in a position to make contact with him on Tattooine, there's no reason to think that she wouldn't know his assumed name as well.