Really, more information would help. I'm not picking on you, 08braithwhaite, honest. It just seems lately questions are posted without providing any information about the gear in question or the size of the asker. The son of one of my friends seems to want to copy what I choose for gear, and I have to remind him that at 6'4", his choices will be different than those of a garden gnome like me.
As for bug nets, if you have a Dutchware Chameleon, you can get a zip-on bug net that has a spreader bar at the head end - keeping the netting away from your face. If you have a Warbonnet BlackBird, you have a shock-cord guy out option that pulls the netting away. If your hammock doesn't have any "built-in" bug net options, there are 3rd party options from Warbonnet and ENO - full coverage nets with zipper openings.
But ... eventually the netting contacts the edge of the hammock, and if your head is also near that edge, it can be disconcerting, especially with any mosquito whine. One solution is to use a small camp pillow between your head and the netting, pushing the netting away a bit. Another may be to treat your netting with Permethrin. It will solve the mosquito problem, but you may still want the netting further from your head.
I don't use the pillow under my head unless the fill is pushed to the sides so it acts more like a cradle (nearly flat in the middle). Otherwise, it tips my head up too much. My usual use of a small camp pillow is to support a knee in order to change things up a bit from night to night. If I want to lie on my side, then I will use that small pillow to keep my neck/head level. But mostly it's either under my knee or used to push the edge or the hammock a bit further away from my face.