It's not the software. The recording software just "routes" the digital data from you soundcard to the hard drive, and sets-up the format, etc.
If your headset is USB, it's the problem. Noise/hiss is an analog problem
(there are exceptions, like 8-bit digital). Nothing on the USB/computer side is analog. Your computer's soundcard/soundchip is not used when recording from a USB device.
And, the micropone preamps built-into computers/soundcards are usually low quality. And, most headsets are designed for gaming/communications and are not music or "voiceover" quality.
If you want professional quality, something like this
is probably what you need. (I'm not recommending that particular mic, I've never used it.)