Solidity – Does Casting a Keccak256 Hash to uint256 Increase Collision Likelihood?

I have a smart contract with 50+ trillion possible NFT names that could be minted (all have unique names), is there any chance that this method could cause a collision of token ID's? –
uint256 tokenID = uint256(keccak256(abi.encode(_tokenName)))

I need to create unique Token ID's for my NFTs that directly correlate to the name of the tokens, this helps with a few other pre-minting verification functions. Such as the example:

1. By using uint256(keccak256(abi.encode(_tokenName))) I can check if the NFT has already been minted by converting the name to uint(keccak256) and look for matching token IDs.

Snippet of function below:

 /**
 * @notice Converts token name string to a unique uint256 for use as Token ID.
 * 
 * @param _tokenName name of NFT.
 */
function tokenNameToTokenId(string memory _tokenName) public pure returns(uint256) {
    return uint256(keccak256(abi.encode(_tokenName)));
}

/**
 * @notice Checks if the NFT has already been minted, returns true/false.
 * 
 * @param _tokenName name of NFT
 */
function nftExists(string memory _tokenName) public view returns(bool) {
    uint256 tokenId = tokenNameToTokenId(_tokenName);
    return _exists(tokenId);
}

If there is a significant risk then I will introduce some additional mappings and go with a standard incremented tokenID.
Thanks