The problem is that a consumer would think that different things are described (or more accurately: the consumer wouldn’t know if the things are the same or not).
There is a way to prevent this¹: give each thing a URI, and in case the things are the same, the same URI.
This can be done with @id in JSON-LD, and with itemid in Microdata.
So a simple case could be:
<!-- markup on the product page,
so the fragment "#this" results in an absolute URI like
"http://example.com/products/foo#this" -->
<!-- JSON-LD -->
<script type="application/ld+json">
{
"@context": "http://schema.org",
"@type": "Product",
"@id": "#this",
"name": "Foo"
}
</script>
<!-- Microdata -->
<article itemscope itemtype="http://schema.org/Product" itemid="#this">
<h1 itemprop="name">Foo</h1>
</article>
In case a property like name has different values, the obvious way a consumer could handle this is to give the thing multiple names. For a feature where the consumer needs exactly one name (e.g., in a rich result), it’s not defined which of the name values will be used. If the consumer is a search engine, it will likely use its already existing proprietary algorithms to handle such cases.
¹ Of course it’s not clear if/how all the various consumers support it. But it’s the correct way to do this, and it’s the only explicit way to do this. Implicit ways include hoping that a consumer understands that identical values for typically (but not necessarily) unique properties (e.g., url, email, productID, etc.) mean that the things are the same. But such an implicit way can of course be used together with the explicit one.