Why are some of the tokens named "zXXX"?
The Zero Exchange "wraps" some of the tokens when they are bridged from their "native" chain to another chain. Once they are bridged back on their "native" chain, they exist again in their original state and are not wrapped anymore. As an example if you are on the Ethereum chain and you use the cross chain bridge to move some ETH to the Avalanche chain, it will be labelled as zETH when you see it inside your wallet connected to the Avalanche chain.
Once you cross chain back a wrapped token to its native chain, it will exit again in its native state. So if you cross chain zETH from the Avalanche chain back to the Ethereum chain, the zETH will become ETH again.
On some other DEXes, like on Pangolin for example, you may see "ETH" displayed on their interface (or in your wallet when you add their "ETH" token) and not a wrapped version of ETH: Under the hood, they are wrapped.
It would have been more appropriately labelled as "pETH", but these DEXes have chosen to not display it to the user as a wrapped token. On the Zero exchange, it's the WYSIWYG ("What You See Is What You Get") principle for full transparency.
If you do find yourself with some tokens on Avalanche that have been wrapped by Pangolin and want to use them on the Zero Exchange (and vice versa), you can use the swap function of one the partners of Zero, Gondola Finance.
Check this FAQ regarding trading tokens on the Zero Exchange and other exchanges.
For the Zero token, you don't see "zZero" on the different chains, because it's native on all the chains that the Zero Exchange supports.