I don't quite understand the concept of an 'akathist' (hymn devoted to a saint). Are these written, one per saint whenever someone is glorified? Are they spontaneously generated over time? I am trying to find the akathist for St. Dorotheus of Gaza and do not know if he has one even.
Hopefully this blurb from this Wikipedia article answers your question:
The writing of akathists (occasionally spelled acathist) continues today as part of the general composition of an akolouthia, particularly in the Slavic tradition, although not all are widely known nor translated beyond the original language. Reader Isaac E. Lambertsen has done a large amount of translation work, including many different akathists. Most of the newer akathists are pastiche, that is, a generic form imitating the original 6th-century akathist to the Theotokos into which a particular saint's name is inserted. In the Greek, Arabic, and Russian Old Rite traditions, the only akathist permitted in formal liturgical use is the original akathist.
In other words I gather that there may not be an Akathist for St. Dorotheus, or there may be one in Arabic that hasn't been translated.
There's no requirement in the Eastern Orthodox Church that once a Saint is canonized other than that there are hymns composed to commemorate the Saint on his Name's Day during Matins, Vespers and Liturgy.
The formal Rite of Glorification begins with a final Memorial Service for the person about to be canonized, after which Vespers and Matins with special hymns to the saint are chanted and the saint’s icon is unveiled. The saint’s life is published and the date of his or her commemoration is established. The other Orthodox Churches are notified of the glorification so that they can place the new saint’s name on their calendars.
These prayers CAN include an Akathist, but don't have to. I'm not even sure a Canon is required, but certainly to complete the Vigil service, troparia, kontakia, stichera, and aposticha hymns are needed. What I gather from the above is that, in modern day, it's a given that enough will be composed to complete Matins, Vespers, and Liturgy for the service of the glorification of the Saint for official canonization.
I would also add that this is not a hard rule. There are many recognized pre-Great Schism Western Saints (St. Patrick, St. Brigid, St. Colmuba, etc.) who, up until recently, had no Vigil hymns composed because it was not a western tradition (though, thanks to the efforts of Orthodox England, this is changing (http://orthodoxengland.org.uk/zliturgics.htm) many of these services are being written/recovered. But there are other Saints, such as St. Gwynllyw the Penitent King (of wales), for whom I know of not even a Sunday Feast Day Troparion that exists (https://en.wikipedia.org/wiki/Gwynllyw).
In the end, the only requirement for a Saint to be canonized in the Orthodox Church is that there is an Orthodox Christian community somewhere that has recognized the sanctity of the Saint's life and chosen to canonize him to lift him up as an example to the world of Christian piety worthy of veneration and emulation.