[The Barrow-Wight]

By the time she secretly joined the army, I don't think Eowyn was seeking glory. After all, it was unlikely anyone would survive to remember her deeds in battle. Instead, Eowyn was seeking her death, as her fight with the Witch King cleary shows.

As for her disguise and who it might have fooled, she was protected from the main mass of the army by Elfhelm, who, no doubt grudgingly, allowed her to come along. She rode along quietly, so as not to rouse attention. And if not for the circle of conspirators around her, her presence would have been known by the King almost immediately.