Is there a specific term in Norse mythology for Odin's self-sacrifice? Norse mythology knows some terms for quite complex concepts, such as "Ragnarök". Is there a term for Odin's nine-day self-sacrifice?

**Nope.**

The story is known only through Hávamál, a piece of poetry from the poetic Edda, in which it takes up two stanzas. The relevant here is stanza 138:

> Veit ek, at ek hekk
> vindga meiði á
> nætr allar níu,
> geiri undaðr
> ok gefinn Óðni,
> sjalfr sjalfum mér,
> á þeim meiði,
> er manngi veit
> hvers af rótum renn.
> Hávamál, stanza 138, from Heimskringla.no

English translation:

> I know that I hung
> upon a windy tree
> for nine whole nights,
> wounded with a spear
> and given to Odin,
> myself to myself for me;
> on that tree
> I knew nothing
> of what kind of roots it came from.
> Source

The relevant word here is "gefinn". This appears to be a normal verb, the Old Norse equivalent of "given". So no, there was no specific term for this sacrifice, at least none that we know of.