Sometimes the letters י-ו seem to serve as a name of Hashem. For example, many authors replace י-ו with טז in a numbering system, presumably so as to not write Hashem's name, similar to replacing י-ה with טו. In many names, י-ו seems to refer to Hashem, as in יוחנן and יונתן.
Where does this come from? Is this name ever used anywhere on its own?
R. Aryeh Kaplan, in his article "Reverence of the Sacred," writes that י-ו is written as טז, not because it's a divine name (unlike י-ה, which Avot DeRabbi Natan 34:2 and others write is actually a biblical name of God). Rather, its lettering is changed because י-ו "resembles a divine name."
This exemplifies our sensitivity to desecrating God's name (other examples include writing BeSiyatta DeShamaya in correspondence or writing Yehudah with a final Aleph - "lest one accidentally leave out the letter Daleth and write the Tetragrammaton").
As for the examples that you mention, it's important to remember that biblical names with weak letters are often abbreviated, but when written in full, י-ו become י-ה-ו names, which definitely include a biblical name of God. For example, in II Sam. 1:22, Yonatan is fully spelled יְהוֹנָתָן and in 2 Chron. 28:12, Yochanan is יְהוֹחָנָן. Thus, such names commonly spelled with י-ו refer to Hashem because their "full" names include a divine name, י-ה.
See the Gemara in Sukka 5a in discussing the Mitznefet, there Tosafot (s.v. Yud Hey) says that even half the name of G-d is considered as if you are mentioning His Name
It seems that perhaps this developed as a minhag or may have something to do with kabbaloh as the yud and vav lettering does not appear in Tanach (as a word unto itself). There are rishonim, most notably Rashi who in various places do actually use the yud and vav abbreviation, and not the tes and zion abbreviation. It may also have to do with using letters of Shem Hashem together (as said to me by a rabbi).
