I guess you are right as it is a h2
In core : ROOT/components/com_content/views/featured/tmpl/default_item.php

I can see this in other parts of code in core like
ROOT/layouts/joomla/content/blog_style_default_item_title.php

etc.
We have 13 itemprop="name" and a few of them are concerned.

To be discussed, please:
Question for me is (because not only Google rules) if these itemprops in com_content should be changed into

itemprop="headline name"

or just

itemprop="headline"

Both are OK and allowed.
Shema org Articles defines "name" as "name of the item".

(I use name as a leading subpart inside headline but that's not the question here. Edit->or is it? itemprop name directly for the pure title, headline for the H tag including link etc.)

References
http://schema.org/Article
https://developers.google.com/structured-data/rich-snippets/articles

New post about the issue

http://forum.joomla.org/viewtopic.php?f=706&t=895734&p=3334312#p3334312

I'm just waiting for an answer before I start a new Pull Reuest ;-)

I use name as a leading subpart inside headline but that's not the question here. Edit->or is it? itemprop name directly for the pure title, headline for the H tag including link etc.

just itemprop="headline":

because it is the headline (h2) of the item (blogpost/article/etc.) and it can be but does not have to be the name of this item (blogpost/article/etc.)

and searchengineoptimizers in times of voice-search (siri/hellogoogle/etc.) might be happy to give an item a different name and headline

and we will get b/c issues if the h2 headline is now both and we might want to separate them later...

I agree with @joo7
If you create the PR, we can test it for you.

Closing as we have a PR for testing see #11410