Good question. I struggled with this when i first encountered some organometallic compounds as well. I think perhaps you're getting bonding electrons confused with lone pairs.
First think back to the octet rule. Ok now think of a nitrogen atom in a tertiary amine. It's got 8 electrons in it's outer shell so it's happy. 6 of those electrons are used in covalent bonding, and the other two "belong to" the nitrogen as a lone pair. So there are 8 electrons around the nitrogen, and the electrons not used in bonding are conceptualized as belonging to the nitrogen atom as a lone pair.
With the d block we have the "18 electron" rule rather than the octet, but the idea is the same. I'll try to stick with your example, though forgive me if I'm not fully clear/correct as I'm a full fledged organic chemist that doesn't deal with many organometallics.
In NiCp2 we have Ni(II) as you said so that's 8 electrons that the nickel atom has. Also as you point out, each Cp- brings 6 electrons for bonding. Thus nickel does indeed have a total of 20 electrons around it. I would argue that only 12 of those electrons are involved in bonding. Each Cp takes up three coordination sites on the metal, so even though we only have two ligands on nickel, we can still think of the nickel as effectively being octahedral. Octahedral means six bonds, and with each bond being comprised of two electrons that means there are 12 bonding electrons. The other 8 of the 20 belong to nickel. Can you call them lone pairs? I'd say sure. I mean these 8 electrons are in the outer shell of nickel and they are not involved in bonding, so conceptually I'd classify them as nonbonding electrons and group them into lone pairs. But that's b/c I'm an organic chemist... You'll note that you almost never see the nonbonding electrons/lone pairs drawn in around the metal of organometallic structures. I've seen it now and then, but it's rare.