Rites of Passage was the first title Robert Laxalt used for The Basque Hotel, which was, after all, a coming-of-age novel.
David Rio, in his book Robert Laxalt: The Voice of the Basques in American Literature, suggests that the "passage" in this book is not simply the protagonist's transition from child to adult, but also his progression "from almost complete ignorance of the significance of his Basque family origins to a gradual assimilation of that background."
On another level, according to Rio, the book "has to do with the evolution experienced by American society during the first decades of the twentieth century, represented in the work by the progress toward modernity of Carson City, Nevada, the city where Pete was born." (pp. 93-94).
The character Pete also struggles to come to terms with his father's low-status occupation (sheepherding) and the fact that his family (the Laxalts as well as the fictional Indarts) sold alcohol during prohibition. This situation made a strong impression on Robert Laxalt. The first chapter of his memoir Travels with my Royal is entitled "Bootlegging Days," and several unpublished essays and writing fragments in the Robert Laxalt Papers deal with the subject. The theme of socially-sanctioned but illegal behavior is central to another Laxalt novel, A Cup of Tea in Pamplona.
The French Hotel was the name of the establishment owned and operated by the Laxalt family in Carson City during Robert Laxalt's childhood, playing such a prominent role in the novel, which would explain his second title.
At some point in the writing and editing process, Laxalt settled on a final title, The Basque Hotel -- perhaps to highlight the immigrant identity theme. The Indart family, like the Laxalts, emigrated from the French Basque Country, but in the United States, the family's Basque heritage was stronger than their French identity.