It’s not particularly difficult to make a donation anonymous in a way that the recipient genuinely doesn’t know who made the donation. Just have a neutral third party handle it. This could be a donor advised fund or a trustee, for example. I suspect this isn’t particularly rare.
That would be part of handling anonymous donations sensibly. The transaction should be between the development office and whatever trustee or foundation gives the gift. The ultimate beneficiary shouldn’t be notified of the donation until, say, the end of the fiscal year, at which point all anonymous donations are aggregated.
