I think an interesting avenue for enquiry to this question would be to look at folk stories and songs related to warfare, to see if specific figures are held up as being particularly talented. This, however, is not my strong suit. I can instead take a slightly different route, in terms of helping with your question, which I think could be illuminating.

In briefly answering your question I would say that yes it is likely. This is because Medieval Europe had a well developed system of testing and celebrating the martial talents of nobles (outside of warfare) which was tournament.

Let's take someone who was a real star in the world of martial prowess: Henry the Young King. Henry was born in 1155 to Henry II of England and was the king's oldest surviving son. Young Henry was crowned during his father's reign but was never really in a position of authority. At his premature death Young Henry was very famous, but not just because of the station of his birth - he was renowned even by the lowlier social strata as a great warrior.

From 1174 Henry was assembling a team of knights with whom he could face the European magnates on the tournament field. In this year he was retaining and outfitting a dozen men for his team, but this number grew as his martial star rose. Henry rapidly became part of a set of nobles who were famed for this expertise and patronage, which included his cousin Philip of Flanders.

Similarly, not only were these wealthy captains well known, but so were their most valued recruits. William Marshal, the greatest knight of his generation, was likewise famous and very sought after. Philip of Flanders managed to lure William away from Henry's team and into his own in 1183, for the price of a year's rent from the city of St. Omer, such were the levels of knights' reputations.

David Crouch remarks that Henry's martial exploits during this time 'gave him an international eminence unsurpassed by any European prince other than his cousin, Philip of Flanders'. He further describes the 'remarkable scenes of grief' which accompanied his death; 'in the countryside and towns his corpse was mobbed by hysterical crowds'. Henry's position at birth had endowed him with the money and opportunity to showcase his bravery and ability on the field, but it was the bravery and ability themselves that had made him so famous and adored, just like his rivals and comrades mentioned above.

'His popularity embraced all levels of society' - Crouch.

We can therefore see that nobles who were renowned within their own circles as martially inclined and skilled were thought of similarly by the 'commoners', such could be their levels of fame and celebration.

Our narrative look at the Young Henry here is from Tournament by David Crouch, which is a very nicely constructed piece of work and is particularly strong on the finances involved for people like the Young Henry. The nature of martial 'celebrity', which I think is the real core of your question, is also featured. Hopefully this helped give a certain degree of indication.

Disclaimer: I am not a tournament historian. My formal training is crusader history, but I felt this example in particular might be close to what you're looking for. Cheers.

Edit: Fortmatting.