Hello! It looks like Neptune has 13 known moons.
TritonNereid
Larissa
Larissa was the next one of Neptune's moons to be discovered in 1981, but they lost it again! Oops. They didn't find it again until 1989 when Voyager 2 arrived on Neptune.
NASA made up for losing Larissa though, because when Voyager 2 found it again, it also found 5 inner moons:
Naiad
Thalassa
(Looks the same as Naiad to me...)
Despina
I think this one looks kinda gross. Apparently it's also referred to as Neptune VIII.
In 2002 and 2003, 5 more moons were discovered orbiting Neptune. These are:
Halimede
(Artist impression) Neso is also known as Neptune XIII.
...And Sao and Laomedeia, which are apparently too diddy to have pictures of.
Hope this has given you some insight. You might find this video showing you the orbits of Neptune's moons interesting: