The name of Charlemagne's first wife is unknown. She was a daughter of Desiderius, king of the Lombards, who was married to Charlemagne to seal an alliance with the Lombards in 770. However, within a year, Charlemagne repudiated the marriage in order to marry Hildegard.
She is often found with the name Desiderata, or Désidérade. The name is the feminine form of her father's name Desiderius, and is sometimes translated to the French name Désirée. However, this is now thought to be an error originating from a single source which was a mistranscription of the Monumenta Germaniae Historica. The name does not appear in any near contemporary record.
The noted Carolingian historian Janet Nelson hypothesized in the 1998 work After Rome's Fall that Desiderius' daughter was in fact named Gerperga. The reasoning used by Nelson hinges on the confusion that many contemporaries apparently had between her and Gerberga, the Frankish wife of Carloman, who was brother of Charlemagne and his co-ruler from 768 to 771. Even Pope Stephen III seems to confuse the two and the chroniclers and annalists seem to believe that Gerberga fled, when her husband died, to the court of her father (she fled to Desiderius, who was definitely not her father). What is definite is that Desiderius and Ansa had three other daughters named Anselperga, Adelperga, and Liutperga. The commonality in the names of their daughters is the ending "-perga". Based on this, the author believes the confusion was caused because the two queens (wives of the two brothers Charles and Carloman) had the same name, namely Gerberga or Gerperga, which are, respectively, the Frankish and Lombard versions of the modern French name Gerberg. 
Born: Before 755. (745 to 755 most likely)
We have no direct way to estimate the birth date of Charlemagne's first wife. There is a presumption that Charlemagne's wives were married when relatively young and that his first wife was most likely in her teens. Her eldest sister was an abbess in San Salvatore in 753, so born by say 735. With three other known siblings, the best estimate of her birth is between 745 and 755.
Charlemagne's his first wife was an unknown daughter of Desiderius, king of the Lombards; married in 770, repudiated in 771." No issue.
The ultimate fate of this daughter of Desiderius is unknown.
Footnotes and citations:
↑ Nelson, Janet. "Making a Difference in Eighth Century Politics: The Daughters of Desiderius" in After Rome's Fall: Narrators and Sources of Early Medieval History, editor Alexander Callander Murray. (Toronto, University of Toronto Press, 1998): page 171-. Books.google.com Preview view
Nelson, Janet. "Making a Difference in Eighth Century Politics: The Daughters of Desiderius" in After Rome's Fall: Narrators and Sources of Early Medieval History, editor Alexander Callander Murray. (Toronto, University of Toronto Press, 1998): page 171-. Books.google.com Preview view
Wickham, C. (1998). "Aristocratic power in eighth-century Lombard Italy." pp.173. Walter A. Goffart & Alexander C. Murray, Ed. After Rome's Fall: Narrators and Sources of Early Medieval History, (pp.173). University of Toronto Press. Google Books.