Ha ha - that is one crazy looking alien - reminds me a bit of a parrot!

I think how you would lay out the head would just depend on whether you wanted the texture to be repeated on the opposite side (if you just layout half) or if you wanted to paint irregular details if you layout the whole head. I would go with the latter just so your alien is a bit more interesting, but either way will work fine.

Also, not sure if you already know this, but when you lay out the UVs, you need to make sure that you get them all within that top right hand square as that will be the area that maya takes the UV snapshot from.