[C#] how can I add data to a csv file?

aaa.csv

a
b
c

aaa.csv

a , aa
b , bb
c , cc

That isn't adding data as rows, that adding data to existing rows.

CSV is not designed for editing: it's purely a text based data transfer format, not a database. And as such, the "rows" are just a lines of text - and text files don't have a mechanism for inserting, removing, or changing text.

So you can't add data to an existing row without copying the data up to each insertion point to a new file, inserting the new data, then continuing to copy, either to the next insertion point or the end of the file, whichever comes first. You then close both files, delete or rename the original, and rename the new file to take the original's place.

If you really want to modify data frequently, not use any text based storage (CSV, XML, and JSON are all examples of text based storage) - use a "proper" database instead as they are designed for such manipulations.