Extract Data Based On Logical Tests

I have a set of data in two columns, i.e. 1) dates and 2) names. Now I would like to post in the third column the name "x" if there is more than 2 years (or 730 days) between the current and the previus observation for name "x".

More specifically:
I would like the code/ function to always include the first "new" name then: 1) check whether subsequent names are equal, if equal; 2) check whether the difference between each obervation and the first "same" name is more than 730 days. The code should also always consider every observation with more than a 730 days difference as a "new beginning" for that specific name.

I have tried to use IF and OR functions but the function becomes too long and it does not quite solve the whole problem. Problems with my function occurs when the names change in column two. That is, my function is not able to distinguish between dates that belong to the same name and dates that belong to different names, when performing the second logical test.

I have attached a short example of my data. The problem is solved manually in the example file, just to give a better picture of what I am actually trying to do (I have a few thousand rows in my real file).