I asked the same question a while back and found two different explanations.....
1) ( the one I most believe)That the name Flamingo was Wilkerson's idea and the story of Bugsy choosing the name was just part of the Bugsy fable.....I found a reference here:

http://www.cardplayer.com/poker-news/14379-men-of-action-bugsy-siegel-billy-wilkerson-and-the-flamingo-hotel

2) I also heard and have no reference that he was planing to call it the "La Rue Vegas" as he owned the "La Rue" in Los Angeles and wanted to divest of the LA property, (or needed to because of his gambling debts and the need to lay low from a LA goon he owed money to) and bring the name to the Vegas property to give the casino a more Euro feel and less like a Wild west saloon as many of the existing downtown Vegas places resembled,