Thank you for your answers.

I already have the eigenfrequencies, otherwise I wouldn't be able to do the MSUP analysis. Furthermore, I am not interested in antiresonances, I just wanted to know what those peaks are called.

As for the downward facing line at resonance peaks, I found the following picture in the book "Noise and Vibration Analysis: Signal Analysis and Experimental Procedures" (Link). There, a damper is used to damp a resonance frequency which in turn creates an antiresonance and two distinct resonance peaks. This is exactly what happens in my plot (it is visible, if one zoomes in very closely). I'm guessing that the chosen damping ratio is simply to high. I'm not quite sure, though, why some lines are longer than others.