Psychologist isn’t a protected title in NL, so she can call herself that. But to become a BIG (registry for health care professionals)-registered psychologist, get referrals from GP’s, and for people to get their visit to your wife compensated by their health insurance, she would have to go through the procedure to have her foreign qualifications recognized, involving several exams, including on fluency in the Dutch language, which needs to be on near native level. See https://english.bigregister.nl/foreign-diploma

I know there’s a difference between being a tourist and a resident, my upcoming plans involve a more extended stay of approximately one year.

On what permit though?

By far the easiest way would be a permit as your partner. You don’t have to be married or registered partners; you do have to prove you’re in a long term relationship: https://ind.nl/en/residence-permits/family-and-partner/residence-permit-for-partner#requirements This permit will also give him the right to work, without needing an additional work permit.

If not on a permit as a partner- he’d need to independently find a job that allows for a permit as a hughly skilled migrant, with a recognized sponsor as an employer, and a salary above threshold: https://ind.nl/en/residence-permits/work/highly-skilled-migrant

As a fresh graduate, that could prove to be quite difficult.