How many wand makers are there?

In addition to Jason Baker's fine answer, we also have this information from Pottermore in relation to the new Fantastic Beasts film. In brief, there are four main makers of American wands.

Shikoba Wolfe, who was of Choctaw descent, was primarily famous for intricately carved wands containing Thunderbird tail feathers (the Thunderbird is a magical American bird closely related to the phoenix). Wolfe wands were generally held to be extremely powerful, though difficult to master. They were particularly prized by Transfigurers.

Johannes Jonker, a Muggle-born wizard whose No-Maj father was an accomplished cabinet maker, turned himself into an accomplished wandmaker. His wands were highly sought after and instantly recognisable, as they were usually inlaid with mother-of-pearl. After experimenting with many cores, Jonker’s preferred magical material was hair of the Wampus cat.

Thiago Quintana caused ripples through the magical world when his sleek and usually lengthy wands began entering the market, each encasing a single translucent spine from the back of the White River Monsters of Arkansas and producing spells of force and elegance. Fears about over-fishing of the monsters were assuaged when it was proven that Quintana alone knew the secret of luring them, a secret he guarded jealously until his death, at which point wands containing White River Monster spines ceased production.

Violetta Beauvais, the famous wandmaker of New Orleans, refused for many years to divulge the secret core of her wands, which were always made of swamp mayhaw wood. Eventually it was discovered that they contained hair of the rougarou, the dangerous dog-headed monster that prowled Louisiana swamps. It was often said of Beauvais wands that they took to Dark magic like vampires to blood, yet many an American wizarding hero of the 1920s went into battle armed only with a Beauvais wand, and President Picquery herself was known to possess one.

Interestingly, from what we know about their unique manufacturing styles, Graves seems to be sporting a Jonkers wand.