There is at least one city mentioned in Tanach named Bes El, written as two words; that name currently belongs to a city in Israel and a number of synagogues and Reform temples. Does that "El" have the status of a shem (name of God), so that one should replace it (e.g. with "Kel") under certain circumstances (e.g., I think, when writing it on a paper that will be put in the garbage, though consult your rabbi for practical guidance)?
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There is a dispute about it (in connection with writing a Sefer Torah, whether the sofer should declare it holy or not).
R. Elazar Fleckeles (Meleches Hakodesh, Lech Lecha 1) suggests that this depends on an earlier machlokes, recorded in the Yerushalmi (Megillah 1:9) and Maseches Sofrim (5:10), as to whether the name should be written closed-up (ביתאל) or as two words. Since the halachah is that we write it as two words, he says, then the second element should be considered holy. (Although he also cites Birkei Yosef (Yoreh De'ah 276:29) that some soferim have a tradition to consider it non-holy, and so he accepts that such soferim should continue this practice.)
Kesses Hasofer states flatly that it is kodesh, and in Lishkas Hasofer there (note 9) he says that this may be true even according to the opinion that the name is written as ביתאל. (Which, I guess, raises the question, according to him, of names like שמואל.)
On the other hand, Beis Aharon states that it is definitely chol, based on Targum Onkelos, which doesn't translate the name (whereas he usually translates the name א-ל as א-להא).
All of this is as far as writing it in a Sefer Torah. I don't know whether this would also affect how it should be spoken (when not saying a complete pasuk).