I think that the question exaggerates the amount of confusion over the names in Wuthering Heights. The convention of the place and period is that women took their surname from their father, and then changed it to their husband’s when they married. Emily Brontë could be certain that her readers would be familiar with this social convention.
The name Catherine first appears in chapter III:
The ledge, where I placed my candle, had a few mildewed books piled up in one corner; and it was covered with writing scratched on the paint. This writing, however, was nothing but a name repeated in all kinds of characters, large and small—Catherine Earnshaw, here and there varied to Catherine Heathcliff, and then again to Catherine Linton.
The reader will recognize that these are the doodlings of a girl considering the possibilities for her future husband; which name is the original is confirmed in the next paragraph:
It was a Testament, in lean type, and smelling dreadfully musty: a fly-leaf bore the inscription—‘Catherine Earnshaw, her book,’ and a date some quarter of a century back.
Note that if this Catherine was annotating her bible 25 years ago, then she cannot be the young woman of chapter II who “did not look seventeen”.
If there is any lingering confusion over the relations between the characters, this is dispelled by Nelly Dean, in chapter IV:
‘He [Heathcliff] had a son, it seems?’
‘Yes, he had one—he is dead.’
‘And that young lady, Mrs. Heathcliff, is his widow?’
‘Where did she come from originally?’
‘Why, sir, she is my late master’s daughter: Catherine Linton was her maiden name. I nursed her, poor thing! I did wish Mr. Heathcliff would remove here, and then we might have been together again.’
‘What! Catherine Linton?’ I exclaimed, astonished. But a minute’s reflection convinced me it was not my ghostly Catherine. ‘Then,’ I continued, ‘my predecessor’s name was Linton?’
‘And who is that Earnshaw: Hareton Earnshaw, who lives with Mr. Heathcliff? Are they relations?’
‘No; he is the late Mrs. Linton’s nephew.’
‘The young lady’s cousin, then?’
‘Yes; and her husband was her cousin also: one on the mother’s, the other on the father’s side: Heathcliff married Mr. Linton’s sister.’
Using only the information in this passage, the reader can draw the following family tree, which contains all the main protagonists of the novel:
It is additionally possible to deduce, from “‘Catherine Earnshaw, her book’, and a date some quarter of a century back” that she must be the Earnshaw who married Mr Linton, the mother of Catherine Heathcliff, and that the ‘Hindley’ who appears in her diary is likely to be her brother, the father of Hareton.
Nonetheless, the duplication of names does stand out as a feature of Wuthering Heights. Most writers are careful to make their characters memorable (for readers who are not paying enough attention) by giving them distinct and distinctive names. But if the purpose of the duplication is not confusion, then what is it?
One effect is to emphasize the symmetry between the situations of the two generations of protagonists. The older triangle of Catherine, Edgar and Heathcliff came to disaster and misery; this creates suspense as to whether the younger triangle of Catherine, Linton and Hareton will end likewise, or whether the survivors will somehow escape the shadow of their parents.
Another effect is to emphasize the social isolation of the setting. The society of Wuthering Heights is so limited that the elder Catherine has to choose between her adopted (or maybe half-) brother and the boy next door, while the younger Catherine ends up marrying both her cousins. And just as potential marriage-partners are limited, so apparently are names:
It is as if, in keeping with the ingrown, self-generating nature of the society, the fund of names that can be drawn upon is too small; there are not enough names to go around. Thus the same first name can serve for both mother and daughter (Catherine); a name originally used as a last name can become a first name (Linton); a single letter, “H,” can obscurely connect as many as three characters (Hindley, Heathcliff, and Hareton). These doublings or overlappings of names reinforce the sense of an unhealthy proximity or likeness between characters who should remain different; they insist upon that general threat of incest that overhangs this society, the threat of a union between characters who are too “alike.”
William R. Goetz (1982), “Genealogy and incest in Wuthering Heights”, Studies in the Novel, 14:4, pp. 359–376.