Ram, Arni and Admin
There are commentaries that make the assertion that Ram and Arni were one and the same person. Thus Zondervan states with absolute certainty that
‘Arni - an ancestor of Jesus in Luke 3:33...[is]...called Ram in Matthew 1:3...’
even though the Greek for the former is arni (arni) but for the latter is aram (aram) which, personally speaking, don’t appear to be all that similar!! Matmor, on the other hand, confirms that the two Gospel writers list different descendants in each of their lists.
The conflict arises because the ‘accepted’ Greek text for both the translation of the KJV (the Textus Receptus) and the more modern versions (the Nestle text) differ at this point, the former having Matthew and Luke’s text harmonised while the latter is as above in the list used for this study (we should note also that the NIV amends the Nestle text to read as the Textus Receptus, finding no reason to disagree with the older reading but making a note that the manuscripts in existence differ widely at this point).
The ‘discrepancy’ isn’t that important (though it probably would be if you had been either Arni or Admin in Luke’s list!) and is one for the scholars to discuss. As Ruthmor writes on Ruth 4:18-22
‘It seems likely that the genealogy is somewhat compressed, with certain names being omitted. NBD dates...Judah...c.1750-1650 BC, with David’s accession c.1010 BC. To cover this span of c.640 years, the genealogy lists but ten names (including that of David)’
There is, therefore, plenty of ‘room’ to include numerous additional fathers without making the list appear to become ‘overcrowded’.
Though nowhere in the OT is there a list that contains either Arni or Admin as the descendants of Hezron or Ram (a point which favours the reading of the Textus Receptus), it could equally be argued that there would be no reason to include these two patriarchs had they not been known to be true and contained within the original (a point that favours the Nestle Text). This discussion, of course, will never be successfully resolved - we need only to note it and move on!
Note also that Hezron was the last descendant of Judah in the Messianic line to have been born in Canaan until the return from the sojourn through the Exodus, Ram/Arni being born in Egypt. We can see this by reference to Genesis chapter 46 which lists the names of the family members that moved down to Egypt from Canaan to settle alongside Joseph and which stops at Hezron (see v.12).