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From:

https://en.m.wikipedia.org/wiki/Genealogy_of_Jesus

Maternal ancestry in Luke

A more straightforward and the most common explanation is that Luke’s genealogy is of Mary, with Eli being her father, while Matthew’s describes the genealogy of Joseph.[40] This view was advanced as early as John of Damascus (d.749).

Luke’s text says that Jesus was “a son, as was supposed, of Joseph, of Eli”.[41] The qualification has traditionally been understood as acknowledgment of the virgin birth, but some instead see a parenthetical expression: “a son (as was supposed of Joseph) of Eli.”[42] In this interpretation, Jesus is called a son of Eli because Eli was his maternal grandfather, his nearest male ancestor.[40] A variation on this idea is to explain “Joseph son of Eli” as meaning a son-in-law,[43] perhaps even an adoptive heir to Eli through his only daughter Mary.[44] An example of the Old Testament use of such an expression is Jair, who is called “Jair son of Manasseh”[45] but was actually son of Manasseh’s granddaughter.[46] In any case, the argument goes, it is natural for the evangelist, acknowledging the unique case of the virgin birth, to give the maternal genealogy of Jesus, while expressing it a bit awkwardly in the traditional patrilinear style.

According to R. A. Torrey, the reason Mary is not implicitly mentioned by name is because the ancient Hebrews never permitted the name of a woman to enter the genealogical tables, but inserted her husband as the son of him who was, in reality, but his father-in-law.[47]

Lightfoot[43] sees confirmation in an obscure passage of the Talmud,[48] which, as he reads it, refers to “Mary daughter of Eli”; however, both the identity of this Mary and the reading are doubtful.[49] Patristic tradition, on the contrary, consistently identifies Mary’s father as Joachim. It has been suggested that Eli is short for Eliakim,[40] which in the Old Testament is an alternate name of Jehoiakim,[50] for whom Joachim is named.