The fantasy cliche of the Mercenary is the lone man who travels from town to town to offer his services to commoners. Historically, in Europe, mercenaries were large organised groups of thousands of men. Was ''lone mercenary-ing'' a thing in medieval Europe? Where does this myth comes from?

There were instances of small groups of armed men seeking employment for military (and non military) purposes. Huge mercenary companies were a structured and common thing very late in the Middle Ages, crossing into the Renaissance and Early Modern Age.

The case of the Varangian guard is very explanatory where a group of Norsemen (either Danish or Norwegian in the beginning), possibly belonging to different levels of nobility, ventured to Costantinople to enter mercenary service to the Byzantine emperor. They might have gone there in small groups centered around a more powerful aristocrat or as more organized bands of warriors.
On a similarly small scale we can find the early Norman knights that ventured in the south of Italy at the turn of the millenium, and that were attested making the pilgrimage to the shrine of St. Michael on the Gargano river in Puglia as early as 1004. They moved around in groups of perhaps a dozen persons and were beginning to be used as mercenaries by all the political forces in the are (aforementioned Byzantines, the Arabs, the Lombard principates etc.), to the point of getting their own kingdom a century later.
The semi-mythic Jomsviking brotherhood seemed to be acting as mercenaries for both the Norse kings in Scandinavia and maybe the Christian rulers of the North Sea area.

On a broader scale, groups of landless nobles (most of whom were second sons) sought employment in groups, both by entering another aristocrat's household by the way of marriage or service as retainer, and by participating to wars waged by major noble personalities. Something alongside these lines could have happened centuries earlier in the Germanic kingdoms of Northen Europe and in Ireland (in a broader sense, those that didn't have a vassalatic structure modeled on the Carolingian one) with bands of freemen organized around persons of higher status in order to earn money and prestige - again the case of Beowulf or, as non fiction, the many Viking expeditions from the IX through the XI centuries.

On the other side, non-warriors as well could be adventurers as we understand them to be.
As later examples, merchants of the XIII century travelled extremely far and sometimes meddled in foreign political affairs. Marco Polo entered service as a diplomat for Kublai Khan for example, poet and intellectual Dante Alighieri possibly fought as a political militant in the civil war in Florence during the years 1308-1311 and earlier, in the battle of Campaldino of 1294. In Northeastern Italy, young men are documented to have travelled the territories of the Republic of Venice during the late 1500s and early 1600s and working as seasonal textile laborers for years, most notably between Venice proper and Padova.