So, is there a special rite or ceremony by which an Orthodox person is received?
Since I’m not that familiar with the Orthodox Church I am not qualified to answer your question.
Since all of the Orthodox Sacraments are valid, and Chrismation does equate to Confirmation (and cannot be repeated), there is really nothing to be done sacramentally for the person you describe in your example. An Orthodox convert to Catholicism is received simply with a formal profession of faith. A documentation of the Sacraments received prior to conversion would almost certainly be requested, and this would be handled simply with a certificate or copy of an official ledger from the Orthodox parish(es) involved.
They just make a profession of faith.
Someone who is received from Eastern Orthodoxy automagically becomes a Byzantine Rite Catholic, not a Latin Rite Catholic. If they really want to become a Latin Rite Catholic (e.g., because they want to eventually seek ordination as a Latin Rite cleric), they would have to petition the Holy See for a formal change of rite.