Has any EA oriented organization tried promoting donors on their social media?

This is interesting! Have other non-EA organizations been doing this? My main concern would be coming off as self-promoting (for individuals - such is expected for nonprofit orgs). I think EAs are particularly conscious about coming across as people who actually genuinely care about helping the world, rather than people who are just doing good for social status.

I also wonder if there is actually a stigma worth fighting around donating to EA and EA-aligned orgs. In my perspective, it seems that the biggest barriers to EA(-aligned) orgs getting the funding they need is: a) not enough big donors know about, or are sympathetic to EA ideas, or b) orgs themselves aren't giving enough compelling reasons to donate, in the form of quantitative data about cost-effectiveness, impact, and the like.

On the other hand, I could see a scenario where I saw on social media that Person A, who I greatly respect, donates to Organization B, and I might be more compelled to donate to them as a result (though this probably isn't a particularly good way to go about deciding where to donate). I think this is part of why peer-to-peer fundraising is one of the most effective funding techniques. (P2P might be a way to accomplish similar goals to what you mention, while bypassing some of the challenges, though it of course brings up different challenges.)

I think I would be more likely to share my donations this way compared to sharing them myself, because it would feel easier and less braggadocious (I currently do not really advertise my donations).