"Gunther (Gundahar, Gundahari, Latin Gundaharius, Gundicharius, or Guntharius, Old English Gūðhere, Old Norse Gunnarr, anglicised as Gunnar) is the German name of a semi-legendary king of Burgundy of the early 5th century. Legendary tales about him appear in Latin, medieval Middle High German, Old Norse, and Old English texts, especially concerning his relations with Siegfried (Sigurd in Old Norse) and his death by treachery in the hall of Attila the Hun." 
"In several instances, Roman officials, legitimate or otherwise, attempted to use barbarian support against the interests of the Roman state. In 411, the defeated proponents of the usurper Constantine III joined the Gallic aristocrat Jovinus in making common cause with the Burgundians of Gundahar and the Alans of Goar on the Rhine river. Subsequently, Jovinus failed to gain the support of the Visigoths and was defeated and executed."
"While Goar and his followers were supporting the empire as allies, other Alans along with Vandals were ravaging parts of Gaul as was the usurper Constantine III. By 411 imperial power in Gaul had reached such a low point that Goar was encouraged to take overt action. In that year he joined with the Burgundian chief Gundahar to raise a Roman named Jovinus to the purple. Jovinus seems to have been proclaimed emperor at Monzen, a town some thirty miles east of the Burgundian headquarters at Waremme and some seventy-five miles east-northeast of Alaincourt (Aisne)."
"In 413 the Burgundians founded the First Burgundian Kingdom (q.v.), located in Gaul (q.v.) with its capital at Worms (the setting for the great medieval German epic, the Nibelungenlied ). In 443 a second kingdom was established south of Lake Geneva, after a defeat by the Huns (q.v.) that cost King Gundahar and 20,000 Burgundians their lives."
"It is clear enough that some of the characters of the common cycles are historical persons. Thus there can be no doubt that Aetla (Atli, Etzel), king of the Huns, is the famous Hunnish king Attila who died in 453. Again the Burgundian king Guthhere (Gunnarr, Gunther), who plays so prominent a part in the stories of Waldhere and Sigurðr-Siegfried, is clearly identical with the historical Burgundian king Gundicarius (Gundaharius), whose defeat in 435 by the Roman general Aetius is recorded by contemporary writers. Of his end Prosper says only that the Huns destroyed him together with his family and nation, and some scholars have denied that Attila had any part in this event. But our knowledge of the course of events on or beyond the Roman frontier at this period is too slight to justify any confident statement on such a point. Of the other members of the Burgundian royal family Gifeca (Giúki) and Gislhere (Giselher) are mentioned in the laws of King Gundobad who died in the year 516." 
"The second portion of the saga — the story of the doom wrought by the heroine upon her husband, slayer of her brethren (the older form), or upon her brethren, slayers of her first husband (the younger form) — is in so far historic that the names of certain personages manifestly coincide with the names of certain historic personages. Thus the Gibich, Gunther, Giselher, and Gemot of the saga manifestly correspond to the historical Burgundian kings, Gibica, Gundahar, Gondomar, Gislahar ; the Atli (older form), Etzel (younger form) of the saga manifestly correspond to the historical Attila; the Kriemhild of the legend possibly corresponds to the the slaughter of the Burgundians at Atli's Court may possibly correspond to the extermination of Gundahar by the Huns in 436. It has been urged that this second portion has its origin in legendary accounts of these personages and events." 
"Gundicarius, King of the Burgundians, is mentioned as a contemporary of Aetius and Attila. His compact with Aetius, who had worsted him in war in the year 435, A. D., is thus recorded in the Chronicle of Prosperus Aquitanus :
"Eodem tempore [about 435, A. D.] Gundicarium Burgundionum Regem intra Gallias habitantem Aetius bello obtinuit, pacemque ei supplicant! dedit; qua non potitus est, siquidem ilium Chuni cum populosuo ac stirpe deleverunt."
Gundicarius' defeat by Attila in the following year (436) is mentioned by Paulus Diaconus in his 'Libello de Episcopis Mettensibus' as follows :
"Eo igitur tempore [436 A. D.], cum reverendus his Praesul vitam cunctis virtutibus decoratum duceret, Attila Rex Hunnorum omnibus belluis crudelior, habens multas barbaras nationes suo subjectas dominio, postquam Gundigarium Burgundionum Regem sibi occurrentem protriverat ad universas deprimendas Gallias suae saevitiae relaxavit habenas."
The same event is referred to in the 'Historia Miscella' by Paulus Diaconus:
"Attila itaque primo impetu, mox ut Gallias ingressus est Gundicarium regem Burgundiorum sibi occurrentem protrivit, pacemque ei supplicanti dedit."
In this account of Attila's subjugation of the Burgundians (436), there is doubtless confusion of the overthrow of Gundicarius by the Huns, serving as Roman mercenaries (436), with the expedition of Attila (451)." 
While there is a historical reference, for these names...
"The precise relationship with the four named individuals is unknown." 
This is where we run into the border between historical records and the Norse Sagas. There, in the Sagas, relationships are given for the names in question, however, the accuracy of the Sagas is another question.
↑ Wikipedia contributors, "Gunther," Wikipedia, The Free Encyclopedia,  (accessed March 21, 2016).
↑ Roman Aristocrats in Barbarian Gaul: Strategies for Survival in an Age of Transition, pg 82 
Bourgogne-310 and Des Burgondes-4 appear to represent the same person because: There are like 3 names very similar, with different mothers or slight difference in dates of death or birth. It is either one person or he named 3 different children with the same name.