I know iso-octane is an exception and is 2,2,4-Trimethylpentane which intuitively contains both iso and Neo groups. But then what is the structure of neo-octane or even is it possible?
There is no fixed "neo-octane" to begin with. If you look at isomers of octane, you will see 4 of them have neo group out of which 2,2,4-Trimethylpentane has been commonly referred to as iso-octane although it contains both iso- and neo- group. Even if we eliminate isomers containing iso- group, we are left with 2,2-dimethylhexane and 2,2,3,3-dimethylbutane. Which one will you consider "neo-octane"?
These non-standard prefixes are not defined in IUPAC, so it is better to define them with their standard IUPAC names to avoid ambiguity.