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I see three questions beneath your one question, and I will handle them each separately.
First of all, they get their name from him because they are believed to be in accord with him on most/all doctrine, not because they get their doctrine from him, although he is of course a highly esteemed and respected theologian. So in that sense, if Calvin taught something different than Calvinists, who cares? Many of them would care, but more because they want to know why they hold a different position than he does than because they need to agree with him. He is not a prophet.
The most important question for a Calvinist is not, "Does John Calvin teach limited atonement?" but rather, "Does the Bible support limited atonement?"
Calvin's views of limited versus universal atonement are controversial. Both sides of the debate claim him. The quotes you provided in the question are sufficient context for seeing why he's claimed by the "universal" side. The article John Calvin's View of Limited Atonement by Roger Nicole concludes, after examining both sides' claims, that Calvin actually held to limited atonement and gives several reasons, mainly having to do with Calvin's strong covenantalism, trinitarianism, and belief in penal substitutionary atonement. Calvin also often stresses that Christ secured blessings "for the elect." None of it is a slam dunk, but Nicole says one passage (from a treatise written against one Tilemann Heshusius) "deserves special attention":
I should like to know how the wicked can eat the flesh of Christ which was not crucified for them, and how they can drink the blood which was not shed to expiate their sins.
His strongest argument, in my opinion, is this:
A historical difficulty appears when we attempt to explain how Reformed thought moved so quickly from Calvinβs alleged endors*m*nt of universal atonement to the very emphatic support of definite atonement by all but one or two of the delegations at the Synod of Dort. What happened in these fifty-five years to cause the Reformed community to make such a drastic shift?
But ultimately, I don't know if Calvin believed in limited atonement or not. There are two confounding issues here:
Calvin used Biblical vocabulary and left himself open to interpretation on some issues in much the same way Scripture itself is open to interpretation.
The controversy hadn't even happened yet! How could he have defined his position on a debate that hadn't taken place? So we're left guessing as to his position. Either his thought is more consistent with one position or with the other, but the question hadn't yet been formally considered. (However, the Wikipedia article does mention that there is support for the doctrine in theologians predating Calvin. But just like him, they didn't seek to define their support or opposition to limited atonement -- they merely held to a theological system that supported it and that showed in their writings.)
From a theological point of view, Calvinism is a systematic theology. John Hendryx of Monergism.com says that it is impossible to deny limited atonement and at the same time affirm unconditional election. R.C. Sproul says that four-point Calvinists always, on investigation, turn out to be "no-point Calvinists." The "L" in TULIP is one cog in a well-oiled machine, as they say.
From a historical perspective, as with all confessional forms of Christianity, time revealed new challenges to the system that needed to be answered. Jacob Arminius placed himself in opposition to Calvin and the system of theology expressed in the Belgic Confession and Heidelberg Catechism. The Dutch church needed to figure out, together, how to respond to his challenge. So they drew up the Articles of Dort, now remembered for giving us the five points of Calvinism, which answered the five points given in the Articles of Remonstrance. The development of the doctrine of limited atonement was simply a fleshing-out of the theological system developed by Calvin and his successors.
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I want to add a small note on this aforementioned quote on Heshusius:
I should like to know how the wicked can eat the flesh of Christ which was not crucified for them, and how they can drink the blood which was not shed to expiate their sins.
In its face value, taken out of context, this is the strongest quote employed by particularists in order to square Calvin on their side. However, it is not without its problems.
First, interpreting this quote as a defense of limited atonement goes against what Calvin already said in that same tract against Heshusius. Pick this statement where Calvin defends himself:
Still he insists, and exclaims that nothing can be clearer than the declaration, that the wicked do not discern the Lordβs body, and that darkness is violently and intentionally thrown on the clearest truth by all who refuse to admit that the body of Christ is taken by the unworthy.
He might have some color for this, if I denied that the body of Christ is given to the unworthy; but as they impiously reject what is liberally offered to them, they are deservedly condemned for profane and brutish contempt, inasmuch as they set at nought that victim by which the sins of the world were expiated, and men reconciled to God.
First point: Calvin makes the obvious statement that the sins of the world were expiated. Limited atonement advocates will balk at this and insist that by "world" here Calvin does not mean every man - but there is no reason to accept this question-begging.
Second point: Calvin is admitting here that in the Lords Supper, Christ is given to the unworthy, and asserts that these unbelievers are justly condemned for rejecting Christ's sacrifice. Christ is given to the unworthy, however they earn a deserved condemnation because they are rejecting the sacrifice of Christ. This makes clear the meaning of Calvin's statement that the sins of the world were expiated. The unworthy are condemned because they reject the sacrifice that was provided for them.
Second, the particularistic's insertion of a limited atonement is completely mislocated. The argument regularly employed by particularists is that Calvin should be interpreted as saying "since Christ has died only for the elect, I should like to know how the non-elect can spiritually participate in the Lordβs Supper". But there is a thing that should be noted:
Heshusius didn't adhere to limited atonement.
Therefore, an argument that pressuposes limited atonement has no effect against Heshusius.
When Calvin says "I should like to know", he is employing a rhetorical device. He is pointing a question to which Heshusius is obliged to answer satisfactorily. Obviously then, Calvin is introducing an argument based on principles espoused by Heshusius himself (something Schopenhauer would call an argumentum ex concessis). If Calvin is arguing from a limited intention in the atonement to a limited spiritual partaking of the Lord's Supper, then the argument would be essentially pointless to Heshusius, and he would not need to answer it.
Indeed, if Calvin ex hypothesi adhered to limited atonement, then this rhetoric argument would provide ammunition to Heshusius. He would not lose the opportunity to smash Calvin on this point - "Oh, that's now so obvious! Your silly view of Christ's presence in the Lord's Supper is a direct consequence of your ridiculous view of Christ's work on the cross! Your views on the Supper are defiled by your corrupt doctrine of the atonement!"
The other possibility would be Calvin doing a systematic defense for limited atonement in order to ground his vision about the Lord's Supper, and in consequence Heshusius would reply with a systematic defense against limited atonement.
But it didn't happen. The quarrel of Supper didn't turn to a quarrel about the atonement.
Therefore, the quote about Heshusius provide few to zero ground for a particularism in Calvin.