That is one form of it.

I think that that is what you would call him in speaking to him--because it is short.

But you would use more of his name in addressing a letter to him; courtesy would require this.

Even then you would not have to use all of it, but only this much: Sri 108 Matparamahansrzpairivrajakacharyaswamibhaskaranandasaraswati.
You do not put "Esq." after it, for that is not necessary.

The word which opens the volley is itself a title of honor "Sri." The "108" stands for the rest of his names, I believe.