Hi Elisabeth, I had read with great interest your article published on the edmund-rice.org website. It too crossed my mind 4 years ago when i read "Risse" and sometimes "Ries" that it was a deformation of "Rice", but just could'nt prove it!
What i know is that Joseph is the general firstname to every male baptised as a catholic in New-France and Marie(MARY) for every female. So Joseph is not a very strong info to link Adonijah. Second thing, the Sulpicians mission of Lac-des-Deux-Montagnes (Lake of Two Mountains, present day Oka and Kanesetake,a Mohawk territory) was created in 1721. Prior to that date, part of the people that went there were from Mission du Sault-au-Récollet, created in 1692 and before there from Mission de la Montagne.
Sieur Guay was a sulpician missionary priest and became the superior at Mission du Lac-des-Deux-Montagnes. As for Father Jullien, do you know his full name? It could very well be that Adonijah was baptised Julien in honor to Father Jullien as i believe the suffix "aire" was the new ending for Dicker and became known as Dicaire because bought back by Joncaire. As Julien Anenharisonrisi is stated to be a chief of prayer in the mission of Lac-des-Deux-Montagnes, this religious thread would make more understandable a baptised firstname as the one of a priest to whom he could deserved his freedom. It also make sense to me.
Something else i came across is a translation of the word "anenharison". Through my readings, i've read in a huron/wendat history book that "anenharison" is huron and means: one who helps a lot of people. Sounds like a nickname for the job of a chief of prayer while the missionary is away,no? But then, why a huron nickname for somebody in a Iroquoian/Nippising/Algonquian mission of Lac-des-Deux-Montagnes? Is it related to is first place of arrival in New France? If the Rice boys were separated was it because the raiding warriors were not just all Mohawks and then a huron or an abenaquis took Adonijah and brought him in his mission?
I think the best person to help you would be Mr Pierre Bernard, a Mohawk genealogist. His e-mail adress should be this one:firstname.lastname@example.org . He made several genealogical parrish books for Oka and others and he kept the indian name as well when available. There were few more Annen-Harisson in his Oka parish "répertoire des mariages"