Hi,
Thank you, that's helpful and it points to caching rather than HikaShop itself.
On every product page, HikaShop rebuilds the breadcrumb with the current product. When it keeps showing the previous product instead, it means Joomla is serving a cached copy of the breadcrumbs module, so the new product name never reaches the page.
To fix it, edit your Breadcrumbs module (Content > Site Modules), open its Advanced tab, and set "Caching" to "No Caching", then save. That forces the breadcrumb to be rebuilt on each product page.
That is almost certainly the difference with your other site, where the module is not being cached. If it still happens after that, turn off the global cache to confirm (System > Global Configuration > System tab > Cache set to OFF) and check whether the "System - Page Cache" plugin is enabled, as that caches whole pages too.