= is an assignment statement, you appear to be confusing this with a ==, the equality comparison operator.
The statements are entirely different:
self.name = name
assigns the value referenced by the local variable name to the attribute name on the object referenced by self. It sets an attribute on the newly created instance, from the value passed into the initialiser method.
The alternative statement
name = self.name
assigns the value of the attribute name found on self, to the local variable name. It rebinds the local name (replaces the old value with a new). Once the method ends, the effects are gone. You are likely to get an AttributeError as the attribute name doesn’t exist on self at that point in time.
If == had been used, then usually yes, name == self.name is the equivalent of self.name == name. However, objects can override how equality is tested by defining a new implementation for the __eq__ method so the two expressions could theoretically produce different results.
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