My understanding is that they were recruited from settlers and raiders who traveled down through the Kievan Rus territories but I just read they were around for Constantinople's fall in the 15th century. Were they still ethnically "Northmen" or was it just a title denoting an elite fighting force by then? If so, when did the switch occur?
They were recruited from a variety of different peoples.
As you noted, the original Varangians (who appear as an elite mercenary force in the early 9th Century around the time of Leo V the Armenian, and later instituted as an official bodyguard by Basil II in AD 988) were recruited from the ranks of the Kievan Rus. However, not even half a century after Basil's death in AD 1025, the Varangians are reported (in Anna Komnene's Alexiad) to have been drawn primarily from the ranks of the Anglo-Saxons in Thule (England). In the Annales of Niketas Choniates, written in the early 13th Century, it is reported that the Varangians of the 12th Century were recruited from various Germanic peoples in the HRE, the Low Countries, and elsewhere. Later sources from the mid 13th and 14th Centuries, unsurprisingly, tend to skim over or ignore the topic of the Varangians, perhaps telling us that while they may have existed, they were a pale shadow of their former selves and may have only fulfilled ceremonial duties (propping up the last vestiges of Imperial glory in the court). At some point in the early 15th Century (with the onset of severe financial troubles and a dire geo-political situation), the Guard ceased to exist. As far as I am aware, there is no mention of them in the Siege of Constantinople in 1453.
Overall, it seems that there was an effort to recruit Varangian guardsmen from foreign lands to continue the tradition, but to say that these men were ethnically "Varangians" would be stretching it. The Guard suffered several notable setbacks, including their near complete destruction at the Battles of Manzikert (1071) and Dyrrachion (1081), from which they never seemed to have fully recovered, leading to recruitment from varied locations in the late 11th and 12th Centuries. Certainly the tradition of "travelling to Grikkland" remained a valid way for Scandinavians to gain prestige and riches into the 13th Century, but it seems to have become less and less prevalent during the Komnenian period, and most especially, after the death of Manuel I Komnenos in AD 1180 and the Sack of Constantinople in AD 1204. Ultimately, it was the decline of the Byzantine economic and political system (the ability for the Emperors to recruit, pay, and preserve their prestige abroad), which led to the ruin of the Guard.