Richard Packham writes the following:
"Pharaoh"
The BoA uses the word "Pharaoh" as the name of rulers of Egypt (Abr 1:6, 20, 26) and says that the meaning of the word (1:20) is "king by royal blood." The first ruler named "Pharaoh" is identified as a great-grandson of Noah (Abr 1:25).
The linguistic problem is that the word "pharaoh" originally meant "great house." It did not become a title for the king until the beginning of the New Kingdom (18th Dynasty), which began about 1567 B.C. That usage is unknown in Palestine until after 1000 B.C. According to Funk & Wagnall's New Standard Bible Dictionary, article "Pharaoh": "It is certain that in Abraham's time the kings of Egypt were not as yet called Pharaohs." At no time in Egypt was the word used as the actual name of any king. Of course, Genesis has the same anachronism (12:15), but no one has claimed that Genesis was written by Abraham or a contemporary of Abraham.
This “argument” can be answered rather easily with the fact that the Book of Abraham, due to its redaction by later Jewish scribes, would contain anachronisms, similar to how the Torah, due to the influences of later scribes and redactors, contain such anachronisms. For more on this, see, for example, Kevin L. Barney’s essay The Facsimiles and Semitic Adaptation of Existing Sources and David Bokovoy on the Book of Abraham Facsimiles and the Semitic Adaptation of Existing Sources (cf. the post How is the Book of Mormon, the Word of God, if it was ABRIDGED and Edited?)
Further, the coupling of "Pharaoh" and "king" occurs many times in the Hebrew Bible: Gen 41:46; Exo 6:11, 13, 27, 29; 14:5, 8; Deut 7:8; 11:3; 1 Kgs 3:1; 9:16; 11:1, 18; 2 Kgs 17:7; 18:21; 23:29; 23:34; 2 Chron 8:11; Isa 19:11; 36:6; Jer 25:19; 37:7; 44:30; 46:2, 17, 25; Ezek 29:2, 3; 30:21, 22, 24, 25; 31:2; 32:2. In these texts, the terms מֶלֶךְ and פַּרְעֹה are juxtaposed with one another; there is nothing wrong with the later redactors of the Book of Abraham and/or Joseph Smith at a translation level, using “king” and “Pharaoh” in like-manner.
More importantly, however, even positing that the current texts reflects the Abrahamic original and not the influence of a later redactor and/or the influence of Joseph Smith at a translation level, there is no issue. More recent discussion of the use of "Pharaoh" in the Old Kingdom supports the Book of Abraham:
The word [Pharaoh] often appears to be associated with the daily life of the living monarch . . . Since there was a close connection between the king and the [Pharaoh], it is not surprising to find that there is some evidence showing that, as early as the Old Kingdom, the term could on rare occasions refer to the king himself, as [Pharaoh] so frequently does after the Nineteenth Dynasty. (Ogen Goelet, "The Nature of the Term [Pharaoh] during the Old Kingdom, Bulletin of the Egyptological Seminar 10 [1989/1990]:90)
Thus the supposed anachronism does not hold up and was refused over a quarter of a century ago as of writing.