Should I write "calling himself in this/that way" here?

In my text I am trying to say, that it is not clear what intentions the person had, by calling themselves in a certain way (let's say Foobar).

My question is should I use "calling himself this way" or "calling himself so"?

Here is my sentence in context:

Many unsuccessful attempts have been made to explain the meaning of Foobar. To this day it is not clear what Mario meant by calling himself so.

Or:

To this day it is not clear what Mario meant by calling himself in this/that way.

Is it clear what this sentence means? I am not sure if a person can "call" himself... Perhaps I am over-thinking it.

I like the "by calling himself in that way" part. As @Hellion said "calling himself so" although understandable, sounds a little unusual.

sounds good to me.

other possibilities are "referring to himself as X" or "referring to himself that way"

Either would work fine.

"…describing himself thus"

might be another, more formal way of putting it - it has the meaning of "in this/that way" but it has the benefit of being terser, tighter.