It’s your story, so of course, feel free to name it whatever you wish. But from my personal view, these names don’t sound much like the nickname for a serial killer.
For a start, Flower doesn’t inspire much fear, and is therefore a little counterproductive to the killer’s role.
Whilst flowers have been used in the past to do with murder cases, e.g Black Dahlia, it’s more specific to a particular one.
Also, the order of the wording you’ve used, with ‘ghost’, ‘phantom’ etc, before flower, it is reading more as a description of the flower, rather than as a link to the killer.
So, take ghost flower, it’s reading like the flower is the main word, and ghost is describing that flower, like the movie Ghost Ship .
Simply switching them around automatically makes more sense to be a criminal name.
So when a character would refer to it, it would read as ‘… the flower phantom.’ Instead of ‘the phantom flower.’
One sounds like a phantom which leaves flowers, the other, a phantom flower.
And on another point, I think that the cross between normal human and supernatural is less likely when it comes to criminal nicknames.
Admittedly the press run nicknames more than cops, given that they don’t like to boost a killer’s ego by naming them, so it could work. But it’s very important to keep a human killer from sounding beyond human, as something more than human, more intimidating or superior. So referring to them as a ghost or phantom sort of goes against that idea.
In general something more like:
Could be more impactful, something that incorporates death and flowers without being as specific. You could also take into consideration the specific flower he leaves, or the reason he leaves them etc.