Bethel meaning in Hebrew and Phoenician and Aramaic 'House of El' or 'House of God' is seemingly the name of a god or an aspect of a god in some ancient middle-eastern texts dating to the Assyrian, Persian and Hellenistic periods.
May Bethel and Anat-Bethel deliver you to a man-eating lion.
The name Bethel begins to appear in theophorous name from the 7th century BC onward. Some, for example Porten (1969, p121), suspect it may be this god rather than the city of Bethel that is mentioned Jeremiah 48:13:
Or to put it another way, the stone at Bethel which was named House-of-God was also a god in itself, a manifestation of the god Bethel.
Bethel appears in Genesis 31.13, "I am the God of Beth-el, where thou anointedst a pillar, where thou vowedst a vow unto me: now arise, get thee out from this land, and return unto the land of thy nativity."
Zechariah 7:2 may give the personal name Bethelsharezer 'May Bethel protect the king'. This is a verse in which translators greatly differ as to whether Bethel means the town of Bethel which sent Sharezer, or that Sharezar and his fellows were sent to the House of God (that is the temple in Jerusalem), or that "they" sent Bethesharezer and his fellows.
Bethel is mentioned, but unfortunately with no details, in Elephantine and Hermopolis papyri. And in those papyri there are also mentions of gods named Eshembethel 'Name of Bethel' and Ḥerembethel 'Sanctuaury of Bethel' (cf. Arabic ḥaram 'sanctuary').
Sanchuniathon mentions the god Baitylos as a brother of the gods El and Dagon. He later says that the god Sky devised the baitylia, having contrived to put life into stones. The reference would seem to be to Bethels in the plural, that is to many stones like the stone in the Israelite city of Bethel which served a housing for God in Israelite belief.
Compare the Egyptian goddess Hathor whose name means 'House of Horus'.