The stereotypical version of an executioner in shows and movies is someone with a hood over their head. Was this accurate, or were their faces shown? If they were hooded, was it common amongst the locals to know who was actually beneath the hood, or was it truly anonymous?
This depends, probably like a lot of things, on the time period we're talking about.
Since I'm most familiar with the executioners (Scharfrichter, lit. "sharp judge", meaning he judges with the sharp edge of the blade) in the German states, I'll focus on that.
There, executioners were considered "dishonest" professions, which made it difficult for them and their families to move in the class system of the middle ages / early modern period (15th and 16th century). Thus, sons usually had no choice but to follow in their fathers' steps and become executioners themselves, leading to "executioner dynasties".
With the profession seen as dishonest, they also had not much choice in terms of godparents for their children and partners for themselves. This would lead to marriage between executioner families, as well as with other professions that were seen as dishonest, like knackers.
Additionally, they had to followe certain taboos - wear special clothing, or sit in certain seats in the church.
So, to answer your question, no, executioners were not anonymous, and were shunned, considered "dishonest" and had a difficult standing in the medieval class system, although they could be quite wealthy.
Sources (in German):