Was it the Cronenberg dimension or the one in which Rick and Morty are presently in now?
The Cronenberg dimension probably
According to the Rick and Morty wikia page (questionable accuracy) states the C-137, the universe that is most commonly associated with the Rick and Morty pair we see is in fact the one overrun by Cronenbergs. Whether or not this is really C-137 we don't know as Rick could've destroyed a previous Earth, however as far as we've been led to believe it is C-137. Morty similarly states that he's the Morty from C-137, but whether this is due to his lack of knowledge or trust in Rick is unknown.
The dimension makes various appearances over later episodes in Rick's memories or other flashbacks.
This is going to be a confusing answer. So let me label the dimensions with a different name, which will help when you read the rest of the answer.
- ND - New dimension, where Rick and Morty jump to.
- OD - Old dimension, the one that gets Cronenberged.
The question now becomes: which of these dimensions is C-137?
ND = C-137?
This seems the most likely, for a multitude of reasons:
- The show has never mentioned dimensions or any of their names until after R&M have already jumped from OD to ND.
- We first hear the name "C-137" from the Council of Ricks (in Close Rickcounters of the Rick Kind). Notice how it happens:
- This takes place in ND.
- The family is eating together.
- The Council portals in, interrupt dinner, and immediately addresses Rick as "C-137". Their first line starts with "Rick Sanchez of Earth Dimension C-137 ..."
- Although not impossible, the Council has never shown to be aware that Rick is from another dimension (OD) than the one he is in (ND). It's highly likely that the Council was referring to Rick by the dimension that he's currently inhabiting.
- On the Jerryboree form, Rick lists his own dimension as C-137. This happens at a point in time where Rick is pretending to be ND Rick.
OD = C-137?
There is little evidence that suggests OD must be C-137.
This is further compounded by the fact that we never hear the name "C-137" while our Rick and Morty are still in OD.
And then there's the fact that the Council of Ricks referred to our Rick as "Rick Sanchez of Earth Dimension C-137". If C-137 is actually OD, that would mean that the Council was aware that this Rick is the Rick from OD (and not from ND, where they came to get him).
The Council couldn't have known that our Rick is from OD.
Later, when they suspect our Rick of being guilty of the murders, the Council of Ricks wants to scan Rick's portal gun to ascertain where he has been:
Some Rick - Scan his portal gun!
Our Rick - Oh, come on. Don't look at another man's portal-gun history. We -- we all go to weird places.
Some Rick - Yes, but it appears you alone have been going to the exact timelines and locations in which the murders occurred.
This directly proves that the Council of Ricks needs to access the portal gun locally before they know where the portal gun has been. This means that they cannot be aware of Rick's travel history before they took him to the Citadel.
This means that when the Council of Ricks entered the scene and addressed our Rick as "Rick Sanchez of Earth Dimension C-137", they must have been unaware that Rick has travelled (as they have not yet scanned his portal gun), which further suggests that they are therefore referring to Rick by the current dimension's name.
It's never explicitly confirmed, but it's highly likely that C-137 is the new dimension that Rick and Morty jump to after Cronenberging their home dimension.
TLDR Ricks are too smart to be fooled by a Rick assuming the role of another Rick, so when they refer to C-137 as his name, that's because he is Rick from C-137.
We don't know
But, we do know that (at least Rick) is C-137 Rick.
From S01E10, Close Rick-counters of the Rick Kind, Rick (C-137) is recognized as "of all the Ricks within the central finite curve, you're the malcontent" with a "history of non-cooperation with the Council." The Council is well aware of this Rick, and Rick is also aware of it: "Why am I the first Rick you pull in every time a Rick stubs his toe?"
If our Rick is just pretending to be C-137, where would he know that C-137 was against the Council, and why would he go along with it? If both our Rick and C-137 were anti-council, it's not like the Council wouldn't keep track of both of them. The cursory scanning Rick did of universes at the end of Rick Potion #9 would likely not furnish this information, and as Rick is anti-Rick, it's not like he'd even bother keeping a database.
Like the database that Evil Morty uses in the same episode to lure Rick into this trap. It was probably EM's plan that Rick would not escape the Citadel, but even after Rick confronts the mind-controlled Rick, EM lays most of it on the line, to how he planned this to set-up Rick.
Although, the Rick database might have only told EM which Rick was best to frame, but not where he was, right? Unless there is a way to find where Ricks are, from Rick's own mouth: "Well, one Morty is enough to hide from the bureaucrats*, but you get [...] a whole matrix of Mortys and put them in agonizing pain and that creates a pattern that can hide even from other Ricks..." And the aforementioned scanning at the end of Rick Potion #9 show that at least our Rick has a way to scan for other Ricks.
Evil Morty knows that C-137 Rick has a history of disagreement with the Council, and knows enough about where to find him to hack his portal gun remotely. It doesn't seem difficult to find where a Rick is then, maybe just where he has been, which is why the Council needed his portal gun to convict.
So why don't we know that the Cronenberg universe is C-137? Because we have no information available to corroborate. We see in S03E08, Morty's Mind Blowers, that Rick and (this) Morty have had to change universes at least once before, but we have no idea how many times before (or since) that they might have. We also aren't sure that when we meet Rick that we are meeting him in his home universe, as previous to the S01E01 Pilot, Rick had been away for four years- it's all conjecture at this point. Rick could be the same Rick from that universe or Rick could have jumped to that universe after probably losing his daughter in his previous universe, given his attachment to Beth (despite his words at the end of S03E03 Pickle Rick, "my access to infinite timelines precludes the necessity of attachment").
Not to mention that Rick seems very capable of pulling off a universe change (from Rick Potion #9), telling Morty that "It's not like we can do this every week, anyways. We get three or four more of these, tops." How would Rick know that there are so few times they could do this? If there are infinite universes, they should be able to do this infinite times, unless there is some knowledge that Rick knows about the process, perhaps because he's done it before?
So, Rick is C-137 Rick, Rick Potion #9 universe might not be C-137, but we just don't have enough information to go on.
*Bureaucrats meaning here the Galactic Central Government
@Flater pointed out in a comment below that Rick fooled Ricks in S03E01. And...yeah. That's 100% a thing. -_-
...But then, S03E07, the Rick & Morty trying to collect funds from our Rick and Morty somehow have on their clipboard that this Rick is the Rick responsible for the destruction of the Citadel. A quote from S01E10 that I was looking for a place to use was ""Ricks have a very distinctive and traceable brainwave due to our genius.", which I guess means that even though the body might be different, the mind of individual Ricks would be the same across body swaps. So, maybe Ricks are fooled by Ricks assuming a different Rick's look, but doing a brainscan lets you know who the real Rick is. I am interested now if C-137 gets used in any other episode of Season 3?
Let's not forget the
"The squirrels realized that morty found out that they actually rule the world"
dimension (which they had to flee from), which was very likely their home at some point after they left their old Cronenberg'd dimension (since Rick references his statement that they can only "do this" - moving dimensions - a few times). So, depending on when this happened, that world was C-137. Or the one after. This is really getting complicated.