‘The pot that calls the kettle black’ is a special case of the fallacy of ‘ignoring valid analogy’.
It could also be regarded as the fallacy of ‘dual moral code’ or of ‘doublethink’.
If someone gets rightly the attribute “pot that calls the kettle black”, he has obviously a kind of ‘dual moral code’ since he reproaches the other person an attribute that he tolerates for himself. A second suitable synonymous name is ‘double think’: someone thinks something for one context and then he thinks the opposite in a second equivalent context.
In the comments to the question, Conifold said that this is not a fallacy, as also hypocrisy isn’t one. — However, I somehow recognize this ‘dual moral code’ or ‘doublethink’ as a case of analogy, since two persons (or in an extended sense things associated with these persons), that are validly analogous in some respect, are compared. But, of course, it is not the fallacy of wrong analogy, but obviously its counterpart: the fallacy of ignoring valid analogy. As far as I know, this fallacy has never been explicitly mentioned before, and the fallacy of ‘dual moral code’ neither.