The appearance of the root /חור/ with the meaning of nobleman, aristocrat, or elder appears mostly in the later books of Tanakh. Melachim I 21:8, 11 and Kohelet 10:17 juxtapose חורים with elders or contrast them with youth. Nechemiah (2:16; 4:8, 13; 5:7; 7:5; 13:17) consistently juxtaposes חורים with nobleman or priests (see also 6:17). Yeshayahu 34:12 and Yirmiyahu 27:20, 39:6 similarly place חורים in the context of royalty and is commonly translated as “nobleman.” In Rabbinic literature חור came to mean freedom (e.g. Gitten 4:4;Targum on Shemot 21:2; Bereishit Rabbah 92). Daat Mikra, however, understands חורים as aristocrats who were free from paying taxes throughout Tanakh (e.g. Melachim I 21:8; Nechemiah 2:16).
However, the original meaning of the root /חור/ appears too have been “white.” In Bereishit 40:16, R. Saadia Gaon interprets חרי as “white bread,” a symbol of royalty (see Ramban).
Yeshayahu 29:22 uses יחורו as pale, and is understood by multiple commentators as being the Aramaic equivalent of “white” (Radak, Metzudot Tzion and Ramban on Bereishit 40:16; see Daniel 7:9). Being pale-faced may be symbol of royalty since it implies that one is at leisure to stay in-doors protected from the sun.
Esther 1:7, 8:15, and Yeshayahu 19:9 (according to Ibn Ezra and Radal; see especially R”I Karo) use חור as “white linen,” especially in the context of royalty (Esther Rabbah on 1:6; see Jastrow on חור). It is possible that חור/white linen is related to, and possible derived from, חור/hole (Rashi on Bereishit 40:16 and Yeshayahu 19:9 relates חור to wicker and nets).
Thus, three etymologies may be suggested: 1) the white bread-royalty connection; 2) the pale-royalty connection; and, 3) the white linen-royalty connection. Either way, it is not surprising that חור is a common name among the royalty (e.g. Shemot 31:2; Divrei ha’Yamim I 4:1; Yehoshua 13:21)
R. Hirsch (Shemot 32:16) threads the disparate meanings of /חור/ into one conceptual whole, and relates it to the well-known rabbinic dictum (Avot 6:2): “Do not read engraved [חרות] but free [חרות], for there is no person who exemplifies freedom as one who engages in Torah study.”
“Now חור means white, free and open, from which we get the meaning of opening and hole. The basic meaning seems to be “unhindered.” Hence: free, open, and the unhindered i.e. unbroken, rays of light: white. So that חרות could also mean “opening” in the sense of the stone being bored clean through, or actually “freedom,” and in this sense חרות על הלחות would mean “in free mastery over the Tablets” and thereby express that ם" וס" שבלוחות בנס היו עומדים. The Tablets did not bear the writing but the writing bore and held the Tablets. Then the sentence in Avot 6:2 אין לך בן חורין אלא מי שעוסק בתורה , that the Torah makes “free,” would be a literal fact, brought home to one’s mind by a glance at the writing of the Tablets. Just as the writing of the Divine Evidence was not only independent of the material but raises the material serving it to its own level of freedom above the ordinary laws of Nature which govern matter, in the same way human beings, who take upon themselves the spirit of this writing and make themselves the representatives of this spirit, are raised, borne and held by the very spirit itself, above the blind force of ‘you must,’ the lack of free will which clings to all matter, i.e. they become “free.” (See Maharal, Derech Chaim, for a similar interpretation).