It's possible that had some kind of legal surname, and it even might have been Kalonymos (although evidence is lacking), but a cursory glances at several sources from the 1920s and 1930s refer to him as "Rabbi Meir Simcha Kahan." I have a hunch that some may have a bit of a desire, even unconsciously, to see surnames like our surnames on great rabbis. Thus, there have been attempts to supply the Vilna Gaon with the surname Kremer, or the Chafetz Chaim with Poupko. In the case of the Vilna Gaon, there are Polish census documents that list him as "Eliasz Zelmanowicz," but surely he had as much sense of himself as "Zelmanowicz" as he did "Eliasz." It was simply a translation of "ben Shlomo Zalman," even though it looks like (and is) a modern Jewish surname, and today's Zelmanowitz surely think of themselves as Zelmanowitzes.
Perhaps some of us forget just how recent and fluid surnames in the sense which we use them were in the history of European Ashkenazic Jews (hereafter just "Jews"). Broadly speaking, they begin around 1800. As recently as before the Holocaust we see that in parts of Europe the surname used by families just weren't so important, and people were regularly referred to by their friends and acquaintances by other markers, such as town of origin, job, or even the street one lived on. By and large surnames were originally foreign to Ashkenazim, and eventually compelled by law and then custom.
I don't know about everyone else, but my last name has been a part of my identity ever since I could remember. I think of my name as being my legal surname as much as I do my first name. But this cannot be the way Jews felt about their surname when it was new, and probably not how my first ancestor with my surname felt about it. The only probable exceptions were people from famous families, eg, Rapoports, "Ish" Horowitzes, Ginzbergs or Rothschilds. Presumably some descendants of the Maharsha who used the name Eidels did not consider such a name disposable, but a gem to cherish. But that wasn't the case in general.
In my recent post on curly peyos the subject was a man called Wolfsohn or Halle. At one time he signed his name Aharon ben Wolf Halle. He was from Halle. Later he wasn't in Halle, so he began signing his name Wolfsohn. It's hard to see how he had any strong identity as either a Halle or a Wolfsohn; both choices were decisions he made as an adult and was in need of a way of identifying himself beyond a vague "Aharon ben Wolf." If he had grandchildren who continued to use Wolfsohn, as begun to happen, then the name became a part of their identity. If he had moved to England he probably would have changed his name to Wolfs, which is generally what Jews did when they moved there. They took their fathers first name, Anglicized it if necessary, and added an "s" suffix.
In Dr. J. J. Schacter's excellent dissertation on R. Jacob Emden, he discusses that surname (pg. 130), and points out that the rabbi himself never considered his surname to be Emden. Writing in 1765 he explicitly referred to himself as "The beleaguered Jacob Israel, called Yavez. I was never called Jacob Emden . . . It is known that I am not from Emden, I was not born there nor do I yearn to see it." הטרוד יעקב ישראל מכונה יעב"ץ ס"ט לא נקרא מעולם יעקב עמדין Indeed, he only lived in Emden from the time he was 16 or 17, and he signed his responsa יעב"ץ. On the other hand, he obviously had some cognizance of himself as being called "יעקב עמדין," being that he is complaining about it. However, whenever he referred to Emden in relation to himself (on title pages, for example), it was in his former role as the ראב"ד of Emden (not that he ever indicated it was a former role). In German literature he was called Jacob Hirschel, after his father. (Or "dem Emdener Rabbiner Jacob Hirschel," although this example from 1789 is from 13 years after he died:
)As for R. Meir Simcha, when he was born in 1843 surnames were not yet deeply entrenched, and certainly one was not part of his identity. With a name like "Meir Simcha" (not a common combination until after he was gone) what further identification marker was needed? For that matter, I highly doubt the Chafetz Chaim thought of himself as "a" Kagan, as opposed to a kohen.
