Gorm's wife was Tyra - of that there is no doubt. But her parentage is even more mysterious that Gorm's. According to an ancient tradition, she was the daughter of an Anglo-Saxon monarch, perhaps King Edward the Elder, who ruled Wessex from 904 to 924.
Snorri, on the other hand, informs us that Tyra was a sister of King Klakk-Harald of Jutland. (This Danish King is certainly not to be confused with the Harald Klak [d. 845], who was befriended by Louis the Pious a whole century before Gorm's time.)
There seems to be more evidence to support the tradition that Gorm's wife was English.
In the first place, Tyra was a Christian. It is far more likely that a Christian princess would have come from England, where the royal family were Christians, than from Jutland, which was still thoroughly pagan despite the early missionary efforts of Ansgar.
In the second place, several of Edward the Elder's daughters were married to royalty from the Continent. One daughter was married to Otto I of Germany, and another to Charles the Simple, the great-great-grandson of Karl the Great, so it certainly is plausible that Edward may have given a daughter named Tyra to Gorm, in an effort to secure peace between England and Denmark. The Anglo-Saxon Chronicle mentions that the Danes in England submitted to Edward, and it is possible that there may have been a marriage alliance between Gorm and the English royal family.
In the third place, the late twelth-century historian - Saxo - tells us that Tyra was the daughter of an English king. (He calls her "the daughter of 'Ethelred'," but then one is tempted to wonder whether Saxo used 'Ethelred' as a title or generic term of all Enlish kings. Ethelred I lived too early to have been the father of Tyra, and Ethelred II came much too late.)
We feel that Saxo, a Dane, was more likely to have his Danish history straight than was Snorri, and Icelandic Norwegian. Saxo states that Tyra "surpassed other women in seriousness and shrewdness, and laid the condition on her suitor (Gorm) that she would not marry him till she had received Denmark as a dowry. The compact was made between them, and she was betrothed to Gorm."
Whatever her ancestry, Gorm's Christian wife seems to have been a kindly woman, and very popular with her subjects. But she was unable to convert her husband to Christianity, and he remained a staunch pagan until his dying day.
[Royal Families of Scandinavia, Flanders, and Kiev]