It is a difficult question to answer because we have so few examples.

One is Guthrum who was baptized as Athelstan. Apparently there were pennies in his Christian name, so at least some must have called him that.

Another is Rollo, who was baptized as Robert. Unfortunately we know even less about what he was called, even though he appears in different texts. One problem is that they are written some generations after Rollo's death, so, was the author really in a position to know? Besides, a writer like Dudo, seems to be unsure, and uses both names. One might add that Rollo in itself is a continental name form, and that Norsemen around Rollo might have called him something else.

A thing to think about is that, in Christian Europe, it is not until the 12-13th century that we can see an explosion in the popularity of biblical names, so, different cultures kept old naming patterns. This infers that people were often given the same name that they had before they were Christians.

Why were some given other names then? A guess is that in that case, the pagan comes from another and possibly hostile culture. In such a situation it is easy to understand that both priest and patron wanted to see a new name, like with Guthrum among persons from Wessex.

But all Vikings can't have been baptized like that, and even if they were, it is quite possible that the new name was more or less forgotten. Since Vikings also settled as pagans, we must imagine that some were later on baptized in an environment that was dominated by their own culture, in which case they probably often kept their old names.

Finally, if we look at the names of warriors under Cnut and such kings, quite a few of them have Norse names, and the vast majority of them must have been Christian. However they became Christian, whether they were born Christians in the Danelaw, in Scandinavia, or were baptized in England, they use traditional Norse names.

It is a hint that cultural environment is the most important factor, and it probably suggests that many a 9th century convert would not get a new name, and even if they did, it didn't stick. The best chance for it to do so, was if a person settled among the Christian foreigners, or if the person was someone special.