Chryco was chosen as it was different from Mopar, and, I suspect, kept part of the company name. Chryco was in use in the late 1930's.
In 1938 Chrysler of Canada started production on 25" block flathead six cylinder engines. With that, Canadian-built cars took a turn toward greater uniqueness in parts. Thus a unique name for their parts.
Not all Chrysler Corp. cars sold in Canada were built in Canada - 1937-1962 convertibles, 1937-1950 eight cylinder models, various low production series, body styles, etc., were imported and parts for these models were carried by Chrysler Parts and were sold in their original Mopar boxes.
With the US-Canada Auto Trade Pact in 1965 auto manufacturers could import parts from the U.S. duty free - and did. Thus the reduced use of Chryco parts on production vehicles but continued to use the Chryco name for parts sold by dealers - and non-dealers. My father purchased a new 1965 Dodge in 1965. No Chryco battery (there were a number of firms that made batteries in Canada) but the Chryco name was on the windshield washer, radiator, and on the box the service department pulled out for the back up lights Dad wanted installed. They were optional in 1965, for the last year. When I think about Dad's 1965 and the battery, "Exide" comes to mind.
Chrysler Canada used to issue a parts book for Chryco "All-Make" parts for Chrysler dealers, non-Chrysler dealers, and service stations that included ignition, fuel and others parts for non-Chrysler built cars and trucks. Even repair panels for quarter panels, rocker panels and a few other areas that were known to rust. In the late 1960's that part of the parts division adopted the Autopar label.
Around 1983 Chryco was replaced by Mopar, and Autopar faded away. I have Chrysler of Canada parts catalogues from 1933 through to 1985, with a few holes here and there. The 1984 and 1985 parts books are Canadian but have Mopar on the first page. The 1982 edition has Chryco on the first page but I do not have the Canadian edition of the 1983 catalogue. Also, the Canadian editions were given numbers with prefix "WM", unlike the long computer number given to the US edition. The 1983 edition I have has the long number, while all the other editions have "WM".
Pioneer Dodge-Chrysler-Jeep-Ram in Mission, BC, still has his Chryco-Autopar sign over his service department entrance.
Will have to remember to take my camera next time I head out to Mission. Who knows how much longer it may be there.