I'm looking at doing something similar myself. Generally a square or slightly rectangular shape is the most versatile, move to more complicated shapes and you have fewer and fewer pitching options, eventually you come to a tent outer which has just one.
For my smaller hammock (an Exped model) which is fairly short I've a 2.7m x 2.4m tarp made by Alpkit, it's their Rig7 model
https://alpkit.com/collections/tarps/products/rig-7, this has tie-outs along each edge at the 1/4, 1/2 and 3/4 points. By using the 1/4 & 3/4 tie-outs it leaves you with triangles at each end that make very effective doors. They don't zip shut in every circumstance but are pretty close.
For my 3.3m (11ft) hammock I'd need a 3.5m x 3m tarp with similar tie-outs.
I'd add pockets at those tie-outs for pole mods. That would also need some form of ties on the underside of the tarp to stop the poles from slipping. The above Alpkit tarp also has a set of mid-panel "lifters", with a bit of forethought and planning these tie-outs and lifters could be at the same point so there'd be only one set of stitching at each point. The doors could also be tied back to these when not in use.
The Rig7 on the ground is big - plenty of room for two people - we use lightweight bivy bags with it for bug protection.
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