For example, the Normans adopting the French language and culture of the time, the Varangians being assimilated into the Slavs, the Gaelicisation of the Kingdom of Dublin, et cetera (without going too much into the Christianization of Scandinavia, which is another topic completely). It just seems odd to me that it wasn't the other way around (Norse culture being adopted by everyone else).
This is generally the fate of conquerors that are not numerous enough to do more than replace the elite of the conquered nation. The Bulgars were assimilated by the Slavid people of Bulgaria. The Manchus by the Chinese, the vikings by the Irish and French, the Huns by the various local groups and so on.
When the conquerors are not many enough to displace the local population, they intermarry, their children start speaking the local language, they start adapting local customs (especially those of the previous rulers, which often existed for good reason) and after a few generations, they are indestinguishable from the locals.