Can you be a post-doc if you secured funding from a private organization to do research at a university in the social sciences/humanities, or do you have to have governmental funding to do a postdoc?
It is absolutely possible to have a postdoc funded by a private organization - there's nothing about a postdoc inherently tied to a particular type of funding. A couple ways this might happen:
- As @Dexter mentions, there are private trusts and charitable organizations that fund research. This can occur either by funding a fellowship directly, or allowing funds from a grant to be used to hire a postdoc.
- There are also commercial companies that have research grant programs in a number of fields. It's entirely possible to use the funding from one of these to pay for a postdoc.
- A private university could directly pay for a postdoc - for example, as part of a professor's startup package.
Short answer: Yes, you can apply for post doc position in university if you have private funding. (Example of such funding is wellcome trust funding for Humanities and social science)
Warnings: You should always check norms with your funding agencies and universities because some times it is possible to have conflict of interest between both.