His Hebrew tombstone says "Mordechai son of Reb Moshe Yehuda Leib". Looking at where he was born and when, I would guess that Marcovich is a patronymic from his grandfather's name "Mordechai" and that he was also named in memory of his grandfather. Surnames were imposed in the early 1800s and in my family they were not consistently recorded for some time in the records, instead they use "son of --" "daughter of --".
So Davidov "son of David".
Similarly, Markovich / Markowitz: Ukrainian, Belorussian, and Jewish (eastern Ashkenazic): patronymic from the personal name Marko or Mark
So to answer your original question, Marcovich was probably derived from a patronymic. Brenner may have been an alternative surname, I suspect from a toponymic (place name). I can look up Brenner.
In records, my family had two surnames documented and/or the patronymic - Kalwaryski (from Kalwariya, Lithuania) and Margolis (an old Hebrew name). Some family members ended up with one and others with the other. And still others changed their name to Levin(e) since they were Levites.
Here's some more info on Mordechai - Marcus from an excellent source on the secular "nicknames" or kinnu'im:
"Of course, _Marcus_ is a Latin name. But just as Latin _Benedict_
(French _Bendit_) can be a kinnui of _Baruch_, _Marcus_ or the shortened
variant _Marx_ can be a kinnui (of type 2) for _Mordechai_ (not the
other way round).
In his book "Die Familiennamen der Juden in Deutschland", Gerhard Kessler lists the following German-sounding equivalents of _Mordechai_:
Mark, Markus, Markuse, Markusy, Markmann, Marx
In his "Dictionary of Jewish Names", Kaganoff says under MARKS:
Jews with a Hebrew name of Moshe or Mordechai often selected
Marcus or Mark as the non-Hebrew name.
I'm sure that the Guggenheimers say the same thing (I was able to
get their dictionary of Jewish family names by inter-library loan
but had to return it; it's a very valuable source for kinnuim.)
There is also documentary of this kinnui-equivalence, for example
in Jacob Jacobson's index of Jewish marriages in Berlin (Juedische
Trauungen in Berlin 1759-1813, Berlin: de Gruyter 1968). There,
_Marcus_ occurs very frequently as a kinnui of _Mordechai_, and
one Mordechai ben Zwi Mirels who died in 1654 in Vienna was also
known as *Marx* Fraenkel."
Brenner is an occupational name. They also evolved into surnames...
1. German: from an agent derivative of Middle High German brennen ‘to burn’, in various applications. Often it is an occupational name for a distiller of spirits; it may also refer to a charcoal or lime burner or to someone who cleared forests by burning.
2. Jewish (Ashkenazic): occupational name for a distiller, from German Brenner, literally ‘burner’