Not quite.
the resolution field should be <empty> if you want it to accurately show "Not Yet Resolved". If you add "Not Yet Resolved" as a resolution value, and you use it, Jira will treat the issue as resolved. It doesn't matter what the text is, if there is something in the field, the issue is resolved. End of story.
However, to set resolution automatically, yes, that's easy. Edit your workflow and look for the transitions "post-functions". Add the one that says "update issue field", it'll ask you which field (resolution) and give you the list, from which you can select what you want. The list will include "none", which means <empty> and will make Jira show the issue as not resolved.
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