Galt is a boy's name meaning "wild boar" in Old Norse and Old English. Galton is a separate name, and the meaning "steep wooded land" is unsubstantiated. In Old Norse it began use as a nickname, a reference to someone who used the strength or ferocity of a wild boar in battle. The name also has a place in Old Gaelic - used to refer to someone from Gaul, meaning "foreigner," and therefore a surname of separate origins (but still one that started as a nickname). Gault is another form of the surname, which has a connection to the Norwegian word gald, meaning "hard/high ground," and it is the name of the archaeological clay formation Gault. If you follow little breadcrumbs there's a bit more interesting info connecting the Gaelic name with the Scandinavian one and adding in a possible Viking and Huguenot twist.
As for namesakes, there may only be one with Galt as a given name: musician Galt MacDermot. But with the last name, there is Sir Alexander Tilloch Galt from Canadian history, Francis Land Galt from American history, Scottish novelist John Galt, and the fictional John Galt from Ayn Rand's famous story Atlas Shrugged. There's also Galt Aureus, a rock band, several cities worldwide, and a British toy manufacturer with the name.
The U.S. has not had any baby boys named Galt, and none with the spelling Gault.