By the help of a co-worker I've figured-out how to solve it:

cypress.config.js should be:

    reporter: 'junit',
    reporterOptions: {
      mochaFile: 'cypress/results/results-[hash].xml', 
      jenkinsMode: true,
      outputs: true,
      testsuitesTitle: 'Cypress Tests' 
    },

and the top of each test file should be:

describe(Cypress.browser.name + '.' + 'some specific headline', () => {

and that's it, and now my jenkins looks like this: