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.
In the treaty between King Esarhaddon of Assyria and Ba‘al I king of Tyre in 677 BC, curses are called down on the Tyrian king if he breaks the treaty, including:
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:
And Moab shall be ashamed of Chemosh, as the house of Israel was ashamed of Bethel their confidence.
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').