Hi Samuel,
It absolutely is the entry template. If the 'Ship To Name' is not selected with the Enter on New option, then tabbing through the Ship to codes will bypass not only the name but also all of the address fields, going to the Contact name. There isn't a need to specify all the ship-to fields with individual options, so it's all or none. Perhaps this option could be renamed to be 'Ship To Info' rather than 'Ship To Name' to be more clear.
To get what you wish, you need to enable Enter on New for the Ship to Name. Make sure to check Security Groups and the Entry Templates there as these take precedence when used.
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Regards,
Softrak Tech Support