No the private address or private key and the public key are derived using a mathematical formula. There are Services out there that attempt to give you a vanity address, but all they have done is generating a mass number of keys and parse the list that they've come up with for some common words names things like that.
The private key is Created from the public key using math that same public cable always produce that same private key and vice versa.
If the private key is made from the public key, what's stopping me from taking your bitcoin address (public key), calculating the private key, and taking your coins?
It is only a one way calculation. The Private Key can get the public key, but not vice-versa.