Mathematician (not historian) here. It is a statistical certainty that ANYONE you meet has a member of their family at one point in history that had that profession. I think you ought to refine your question to something about whether surnames were originally created based on profession, or maybe more specifically if you followed people's names up only through each father whether you'd get to that profession (which is still pretty likely but much less so).

Here's my reasoning. Assume that births happen on average to people aged 25. (This is pretty conservative; smaller ages give an even faster explosion of people.) Then 25 years ago, you were born to 2 parents. 25 years before that, they were born to 4 grandparents. ... 500 years ago, you had 1 million (2^(20)) ancestors. 1000 years ago, you had 1 trillion (2^(40)) ancestors. Of course this isn't possible, and the flaw in my model is that it assumes no interbreeding at all, even between very distantly related people. But still, you can see that the exponential growth effect is so powerful that one or two thousand years ago a huge fraction of the world's population would be your ancestors. This is mitigated by the fact that people tended to breed within their own race, class, geographical location, etc, but you'd still end up with a huge number of people, and even breaking those rules just occasionally would still be enough to contribute a huge number of ancestors' DNA.

In contrast, if you follow up only the male branch you only get 4000 people over the last 1000 years. As I said, 25 years was pretty conservative so you probably get more, and this is already enough that one of these professions is still fairly likely.