Within the Bitcoin ecosystem where are wallet addresses stored/reserved? I understand that Bitcoin is a distributed system based on the blockchain, and I understand that transfers/transactions are stored in the blockchain, which exists on many servers around the internet.

But where are wallet/account addresses stored?

I understand that there are different kinds of wallet apps, local, online, etc. But the number/string that represents the wallet address within the Bitcoin ecosystem: where does that primarily live? When you create a wallet and produce that address number, do you take dibs on it in some way such that nobody else can get the same address number? What prevents duplication? Is there a null transaction recorded in the blockchain everytime a new wallet is created for the purpose of taking dibs on the wallet address?

I have no idea what I'm saying or talking about--please elucidate!
When you create an address, it is stored in your wallet. It is not recorded on the blockchain until someone executes a transaction that includes the address.

It is not necessary to reserve your address since it is statistically impossible that someone else will generate the same address (with some caveats, see below). Here is what happens when you create a new address in your wallet:


Your private key (for spending funds) is derived from a random number between 1 and 115792089237316195423570985008687907852837564279074904382605163141518161494337. Assuming the number was truly random, you don't need to worry about someone guessing this number since the number of possibilities is so ridiculously large.
The matching public key (for receiving funds) is derived from the private key in a way that is irreversible, and is used to generate the address where you can receive payments. There are 2^160 possible addresses (1461501637330902918203684832716283019655932542976).
The private and public keys are saved together as a "pair" in your wallet.