Like other western holy people who lived after the Great Schism of 1044, Anslem is not recognized as a saint by the Orthodox Church.
Once the Schism occurred the door was basically closed for new saints from the West. But we should be aware of another issue besides this fact: Anselm is regarded as a founder of scholasticism, which is not appreciated in Orthodoxy as in Catholicism. The Orthodox wiki timeline has this to say about his contribution:
1098 - Anselm of Canterbury completes Cur Deus homo, marking a radical
divergence of Western theology of the atonement from that of the East.
Anselm also defended the Roman use of the filioque clause, the main theological bone of contention in the Schism. Thomas J. McKenna writes in the St. Anselm Journal](https://muse.jhu.edu/article/737780):
Anselm developed his defense of the filioque in the context of the
long struggle between Rome and Constantinople. He had developed a
preliminary defense in earlier treatises, notably the Monologion
(1076), but he developed his most extensive and rigorous defense in
his dispute with the Orthodox representatives at the Council of Bari
in 1098. He published his account of the dispute in the De Processione
Spiritus Sancti (1102).
I can find no comment in Orthodox sources regarding Anselm's Ransom Theory, Moral Influence Theory, etc. What is clear is that Orthodox theology is more meditative and less concerned with Aristotelian logic than scholasticism. Its approach is more optimistic about human nature and focuses not on original sin or "ransom" theory but on theosis (divinization), which, unlike Anselm:
...assumes that humans from the beginning are made to share in the Life
or Nature of the all-Holy Trinity. Therefore, an infant or an adult
worshiper is saved from the state of unholiness for participation in the Life
of the Trinity — which is everlasting.
Conclusion: Anselm is a Saint in the Catholic Church but is not recognized as such in the Orthodox Churches. Indeed few if any Catholic saints canonized since 1044 are recognized by Orthodoxy.