Ansuz is the clearest single demonstration that rune names were not fixed and that the meanings attached to them moved with the language.
Three names for one character
The reconstructed Elder Futhark name is *ansuz, a god of the Aesir. The asterisk is doing work: no source from the Elder Futhark period gives us the name. It is reconstructed from later evidence.
In the Younger Futhark the name is oss or ass, still a god.
In the Anglo-Saxon futhorc it is os, and the Old English Rune Poem glosses it not as a god but as the mouth, the source of speech, the support of wisdom and the comfort of counsellors. The Old English word os did mean a divinity, but the poem is plainly reading it as Latin os, mouth.
Why the shift happened
The Anglo-Saxon poem was written by Christians. A stanza celebrating a heathen god was not usable; a stanza celebrating eloquence was. The rune kept its shape and its sound and acquired a new subject.
The same pressure is visible elsewhere in the poem. The rune whose Elder name is reconstructed as thurisaz, a giant, becomes thorn in Old English, a plant. The rune reconstructed as kaunan, an ulcer, becomes cen, a torch.
What follows
Modern rune divination generally reads Ansuz for the divine word, inspired speech, Odin, and messages, which is a sensible synthesis of the god-name and the mouth-gloss, and it is a synthesis. It combines two readings that come from different centuries, different languages and different religions, and treats them as layers of one meaning.
That may well be good practice. It is not a recovery of what a fifth-century carver had in mind, and no one is in a position to say what that was.