When do I use a footnote in a thesis and when do I use parenthesis for extra information?
This is mostly about the reader's flow. Something that is parenthesized is something you expect the reader to actively read, but you're signalling that it's secondary information. The main drawback to parentheses is that if the text in them becomes too long, the reader has to work very hard to remember the main point you're making. You're essentially talking about a lot of unimportant stuff while you have an unfinished, important sentence going. So make sure you put only short, simple things in parentheses. 

If you put something in a footnote, you're signalling that the reader should skip it on first reading and they should only investigate if something is unclear, or if it's a second reading and they need all the details. The drawback to footnotes is that they are often more tantalising than they should be. While the reader should ignore them, they are too curious, and break their concentration to look up the footnote. This pulls them out of the text for something they were supposed to ignore.

On the whole, try to avoid both as much as you can. In your example, ie. this method is also known as X, parentheses should be fine and a footnote is probably overkill. However, you could also consider finishing your main point first, and moving the parenthesized statement to the end of the paragraph as a full sentence. That way the reader can finish absorbing the primary information unencumbered by details, and gloss over the aka's once the hard work is finished.