Vietnam hotels are almost unique in the world, in that they require guests to turn over their passports when checking in.
Vietnamese law requires hotels and hosts to report any foreign guests to the authorities, so hotels dutifully will collect your passport, record your particulars, hand over this information to the police, and give you back your passport as soon as they can (which can be anywhere between a couple of hours to overnight).
This process might take longer than you're comfortable with - if that happens, politely request the return of your passport. My passport took longer-than-usual to return to me when I stayed at Victory Hotel in Hue, but they were rather apologetic when it was returned to me (slightly soggy, too). I took it in stride; didn't ruin the stay for me at all.
If you want to find out more about Victory Hotel, you can read my Victory Hotel Hue review, or find more hotels like it in my Hue Budget Hotels article.