How to combine bins of my DFT I have a time series and apply the FFT to get a spectrum.

Let's assume that my sampling frequency and the length of the time sample are chosen such that I end up with a $\Delta f = 0.1$ Hz.

As this is still rather noisy, I'd like to change $\Delta f$ to 0.5 Hz a posteriori. 

How do I combine the fourier components of the adjacent bins? Am I right to just sum them? Or do I take the square root of the sum of squares?
Is there a term for what I am trying to achieve, so that I can find some references on my own?
There are different methods for doing what you want.
But first i have to tell you power spectrum density (PSD) is real and positive and you have to obtain it from squared FFT of signal or from FFT of signal's auto-correlation (FFT of auto-correlations is always positive).
To reduce noise you could apply some damping window on your signal. This method is called modified periodogram.
Also you could divide your signal to smaller segments and find PSD of each segment then find average of PSD of each segment. This method is called Bartlet method. 
Also your suggested method, summation of adjacent bins or applying moving average works too (you must apply it on PSD).