I'm not so sure about that, don't forget that Galadriel was close friends with the maia Melian, wife of Thingol. Knowing one Maia in "disguize", might very well be usefull to recognize another maia.
Melian wasn't in disguise, she was a Maia in a human form. But it wasn't really a secret : every one knew Elu Thingol married a Maia. And she and Galadriel met after Galadriel left Valinor, so after she possibly met Olorin.
Círdan recongnized Olórin as the greatest of the Istari and gave him the elven ring Nenya. Círdan told Elrond (who also had a Ring) about Olórin, and I'm sure Elrond would have told Galadriel about such an important matter as one of the rings of power shifting hands. Even if she didn't regonzice Gandalf as an Maia, and if she hadn't heard it from Elrond, then she would at least sense that he had Nenya.
Cirdan didn't really recognize him as a Maia, he only saw (before no one saw deeper and further than him) that Gandalf was the wisest of the Istari who arrived at Mithlond and that he would have a lot of trouble and work coming his way --- that's why he gave him Narya (not Nenya).
Anyway, i was asking myself if Galadriel would have recognized Olorin as a Maia if they met in Tirion, not in Lothlorien.
I am pretty sure Gandalf visited Lothlorien soon after he arrived in Middle-Earth and told Galadriel he was sent by Manwë and Varda.
nn[Edited on 7/12/2003 by virumor]
Give up the Halfring, she-elf...