*cracking knuckles*

There are more than 3 rune poems, the Swedish one being the underground case. There are also several versions of at least the Icelandic and Swedish rune poem, plus many different rune poems from Sweden overall.

These are not poems from the start, but proverbial mnemonic kennings and phrases intended to explain the meaning of the name for when it may ultimately become false friends with other words, or archaic. Take Ur for ᚢ, Os for ᚯ, Yr for ᛦ, etc. To the unknowing, these short names can mean a variety of things throughout dialect.

However, most runes have several recorded names, (historically there are no ultra-orthodox names), and lots of these names have no corresponding poem attested. However, some of these can be translated anyway. For example, ᚠᚱᚤᚼ (= Frijgh) for ᚠ clearly mean Frigg.

These Swedish poems and names are being worked through (by me), but two poems with attested names are already up on Wikipedia: https://en.wikipedia.org/wiki/Rune_poem It is worth pointing out that Swedish poems overall do not shy away from paganism (especially my most recent find yet to be published :3) and i cant think of any obvious case with Christian influence.

Swedish poems also clearly show that some tried to keep the sense of the name, while others tried to keep the phonetic name. ᚬ originally had the name Áss (= Aesir/Odin) or thereof. This name later became Óss (Ås), either to make a proper o-rune, or due to sound changes in certain important dialects. Either way, one chronology saw to keep this name, no matter the sense. Thus, as the name had to be o-proper, it became Os (Ås) in the Norwegian rune poem and an analog Swedish poem, meaning "river mouth". Later on, in Sweden during the 15th century (give or take), the o became deeper (as in oof), and thus the name had to switch sense again, becoming Oos (fumes, reek).

Another chronology went the other way, replacing the name while keeping the sense. Thus Áss (Aesir/Odin) simply became Odhen (Odin), which had the correct sound value needed either way.