Firstly, I agree with others here that you should seek advice from a senior person in your department prior to making any decision on this matter.
Look, your work must have addressed questions not answered until now - otherwise you would not have been allowed proceed with it. You used relevant techniques, organized your work well, reported your data honestly, interpreted your results fairly and drew reasonable conclusions in the context of that field of research.
That is all that any honest PhD candidate can do, whichever university they go to. With hindsight, you may feel that another approach or even topic might have yielded more "exciting" results. As you suggest, more "exciting" conclusions can help a paper to be published more quickly or in a more prestigious journal; some PhD derived papers have even made their way into the annual proceedings of the Royal Society. But that is in the hands of fortune. The main thing is not the "exciting" nature of our work but its validity. What you regard as humdrum work may well be relied on by future researchers who would otherwise have sought the same answers as you did: with your findings published, they can include or exclude various other hypotheses, save time and money and redirect their work towards other related but as-yet unmined questions.
There is no sense in being ashamed of our honest work, still less of feeling you haven't maintained the accustomed standard of your department or research group. The noisies in a team are seldom the most valuable. And excess humility does show a lack of pride in honest endeavor. The university provided a major share of the support for this project. It is reasonable for them to be listed as the affiliated organization. In fact it may well be that you would have no chance of being published in many journals without detailing your affiliation, however exciting your conclusions would be.
I think that you have to submit your work for journal publication and that you must not do so anonymously. The conference submission is another thing. At conferences there's often an unhealthy group dynamic and people with no interest in certain papers at a session nonetheless remain there exuding their boredom. The "exciting" papers of course seem to get all the attention. On the one hand, I could understand you wanting out of this; on the other, non-attendance resigns you to miss meeting other honest triers - some of whom will be today research managers and potential employers. But please revert to more experienced people - not solely your supervisor and HoD - for their opinions on this.