Culture-conversion is done on a province-by-province basis.
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When available, the button next to the province's culture will be coloured, and you can click it to view of a list of the cultures you can change a province to. You can always change it to your nation's primary culture (Dutch, in this case), or the culture of an adjacent province. A province can always be changed back to it's original culture from 1444, if it's been changed. Either way, it costs Diplomatic power.
Westphalian is a lower priority for changing though, because it's part of the same
Culture Group (German) as Dutch. Same-group cultures have reduced penalties. Either way, the penalties are removed if you accept the culture. The colour of the culture name on the province indicates its effects: Green is a primary or accepted culture, with no penalties. Yellow is a (Non-promoted) culture in the same group as your primary culture, with small (-15%) penalties to manpower and tax income. Red is a (non-promoted) culture from a different group, with larger penalties to manpower and tax, an extra 2 unrest, and a penalty to local missionary strength.
If you enter the culture mapmode, it will show the culture groups on the map. If you have a province selected, the map will show the individual cultures in that group.
I mentioned you can change the culture in a province to something other than your primary culture. If you're wondering why you would: normally you wouldn't, but the main reason people do is when they want to change their primary culture. You need the majority of the development of the provinces in your states (but not territories) to be the target culture in order to change to it. The most common reason for culture-switching is unlocking decisions to form other nations. Switching to Dutch to form the Netherlands, as an example.
Generally, province-culture isn't a super-high priority: It's usually not worth avoiding diplomatic technology or ideas to change a province's culture instead. But if you have an excess of diplomatic points, it is an option to spend them on.