Hi,
I'm not clear on the situation. However, I suppose it's something linked to you having another field with the translation you don't want, like the alias.
Put the text you want in the main "name" field of the product.
Then, go in the HikaShop configuration, under the "Languages" tab.
There, edit each language.
On the right side of the screenshot, you'll have the override area, where you'll see all the translations you've entered.
So suppose that in the main name of the product, you've entered "my product", you need to search for the corresponding translation key, which is: MY_PRODUCT
There, you'll see a line like this:
MY_PRODUCT="text"
And you can directly change the text there for the current language you're editing.
You should then have the result you expect.