Distinguish Person's names from Organization names in structured table column

If you have reason to believe that all entries are sufficiently known (i.e., common brands and celebrities), you could utilize distant learning approaches with Wikipedia as a source.
Essentially, you search for each entry on Wikipedia, and utilize results from unique search results (i.e., searching for "Tesla" would lead to at least two uniquely different pages, namely the auto company, and the inventor). Most importantly, each page has assigned category tags at the bottom, which make it trivial to classify a certain article by using string matches with a few synonyms (e.g., Apple has the category tag "Companies liste on NASDAQ", so you could just say all categories that have "company"/"companies" in the name are referring to articles that are companies.

With the results from the unique search terms, you should be able to construct a large enough training corpus with relatively high certainty of having accurate ground truth data, which you can in turn use to train a "conventional" ML model on the task.

Caveat:
I should note that it gets significantly harder if you are doing this with names that are relatively unknown and likely won't have a Wikipedia article. In that case, I could only think of utilizing dictionaries of frequently used first/last names in your respective country. It is certainly more prone to false positive/negatives (e.g., "Toyota" is also a very common last name in Japan, although Westerners likely refer to the car maker). Similarly, names that are less common (or have a different spelling) will also not be picked up and left out.