The official moniker for Samsung's foldable smartphone remains unknown. The company recently trademarked the “Samsung Infinity-V” moniker in South Korea under the smartphone displays category. It feels like an appropriate name for the device given the branding that Samsung is already using for its near bezel-less OLED displays.
The company may be considering additional monikers along the same lines. It has registered several similar brands in the United States. They include Infinity-Flex, Infinity U and Infinity-O. Samsung has also registered Infinity-V in the US.
Infinity-Flex and other possible names for Samsung's foldable smartphone
Samsung markets its 18.5:9 displays as Infinity Displays so it would make sense for the panel in the foldable smartphone to be marketed as such. Infinity Flex appears to be the most fitting moniker for this device. It would have a flexible/foldable OLED display so this brand name will certainly make sense.
The registration for all four monikers mentions that they're meant for “Mobile phones; Smartphones; Displays for mobile phones; Displays for smartphones.” It's unclear what the other monikers may be used for. Perhaps Samsung is only protecting them right now and could use them for other devices in the future once it introduces additional models in the foldable series. That's just speculation at this point in time, though.
We exclusively reported last week that the foldable device may be a part of the Galaxy F series. Samsung is already testing the firmware for it in the United States. The company will likely showcase the unique UI and some of its features at SDC 2018 later this week.