Per the JASO documentation, it sounds like anyone who meets the requirements that are submitted and vetted through JASO can put the registration logo on the bottle if they want to. I searched the Sep 2025 JASO registration list (link given earlier) just now, and only saw these two Mobil oils, but they look to be a variety not sold in this country.
I have noticed that oil sold through Honda, Yamaha, Kawasaki and Suzuki will have the JASO registration logo on the bottle. My example of the Castrol Power 1 given earlier in this thread shows it can be in the JASO registration list, but won't have the registration on the bottle.
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