The Planeteers are never given 'full' names in the canon universe. Fans of the series have instead given them names which have slowly become accepted, sometimes to the extent that people confuse fandom with canon.
Wheeler is possibly the Planeteer given the most names by fandom. There is canon evidence that Wheeler is actually the Fire Planeteer's surname. In the episode Talkin' Trash, a character remarks, "That's that lush Wheeler's kid," referring to Wheeler's father. This would indicate that Wheeler is a surname and both the Planeteer and his father go by it. (Incidently, Wheeler's father is not named in the canon universe, though there is a strong belief within fandom that his name is 'Nick'. The original source of this belief appears to have vanished, however. There are no references to this name within canon.)
There is also an episode in which Ma-Ti refers to Wheeler as "J.W.", creating the possibility that 'J' is Wheeler's first initial. Many fans have used this in their Fan Fiction, often referring to him as 'Jason', 'Justin' or 'James'. Other fans choose to create their own first name for Wheeler, or to use 'J' as a middle initial.
It is possible that Ma-Ti was simply playing up to the disguise he and Wheeler were operating under at the time, and that the initial 'J' has nothing to do with Wheeler at all.
Linka is never given a surname, but it is generally accepted in fandom that "Linka" is a shortened version of a longer name. This is not supported in canon - everyone calls her Linka - but it is not out of the question, as many Russian names have 'Linka' as a shortened or affectionate version. A simple google search will lead to further examples.
Like the other Planeteers, Gi's full name is never revealed. A google search for her name indicates that 'Gi' has roots in Korean culture, but also that it is used predominantly as a male name. Thus, Gi's actual homeland is still very ambiguous. Fanfiction has her hailing from South Korea, Thailand, China, Japan, etc.