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I'm going to argue that Eppo Bruins does not qualify for this, since he has "temporarily ended his membership" of the ChristenUnie, and he has explicitly stated he will be cabinet minister representing NSC and not CU.

’Het moet duidelijk zijn dat, als ik minister word, dat namens NSC zal zijn en niet namens de ChristenUnie, de partij waar ik tot nu toe met hart en ziel lid van was.’

Source: https://www.nd.nl/nieuws/politiek/1228044/eppo-bruins-zegt-lidmaatschap-van-christenunie-op-partij-moet

I have not been following the news, but yes, what counts is in what party's name someone takes the position, not any previous membership/association, even if very recent.

See also:

"Bonus: New minister or state secretary position is introduced"

Will this resolve positively if there is a name change? Or a small redistribution of responsibilities? Or if there a minster for housing and zoning in a separate government department?

"just" a name change: no. The other two I think would depend on the details. If you're trading on a specific proposal, do you have a link to an article so I can take a look?