Which country issued the passport? And does the details page only have a single line for names, rather than showing given names and a family name/surname on different lines? And how does the name appear in the first machine-readable line?

In a Chinese (or perhaps more accurately Hong Kong Chinese) context, I'm used to seeing names in different formats depending on context. Someone might have the Chinese name Chan Wing Yip, and also have an English given name of Alan. He might be Chan Wing Yip in some contexts, Alan Chan in others and Alan Wing Yip Chan in further situations. But in Hong Kong, it would be common to find the name rendered in official documents (eg a passport) as surname Chan, given names Wing Yip Alan.

I could see how it could then be objected that a ticket in the name of Alan Chan does not match the passport surname / passport first name combination (although Wing Chan would).

My mother has a further variation on this by sometimes using her married surname on its own, and sometimes using a surname comprising her married surname followed by her maiden surname. So she has two official names: one is in the form surname Lam, given names Jane Yee Wah, and the other is surname Lam Yeung, given names Yee Wah Jane.

Fortunately, she has one passport in each name and travels carrying both.