I have 2 pair and both have their name on them: 1) Arizona soft footbed with oiled leather that have the name in the leather by the arch and in the footbed along with the size and a helpful symbol that identifies the width (open foot outline is wide/regular; solid/filled in foot outline is narrow/medium and they are quite narrow in the toes); 2) Milano shearling has the name in the nubuck by the arch and a fabric strip sewn atop the shearling footbed with the size and width symbol. Happy Feet stores (and online) are authorized to sell them and give generous point rewards and often have sales. I started there to get fitted. Birkenstock online offers discounts to members; for example, my Milano Shearlings are $170. and I paid $87 (just sign up for emails to be a member). My ortho surgeon recommended the Birkenstocks to me when I had a toe injury and needed arch support and open toes. I couldn't believe how much my aching, arthritic feet loved them. Still do! I like having a back strap which is why I got the Milano.
Birkenstock is picky about who can sell their shoes and don't authorize retailers who are only online, including Amazon, so there are a lot of knockoffs and third party sellers. And some retail stores, such as Macy's, can sell them, but carry the narrow ones only/for the most part. PS I also got the real Birkenstock socks from Birkenstock.com and they are wonderful! I tried every sock I owned first, but the real B socks are also worth the money--you forget you have them on. I machine wash them, but hang to dry.