Once one deploys a crowdsale contract, can the variables like token supply, name, symbol be modified at a later date?
That depends on the contract code. If the contract has functions that change the variables holding these parameters then it's possible to change them. So it's highly recommendable to look at the code before investing in an ICO or buy tokens.
Please see example here: https://github.com/TokenMarketNet/ico/blob/master/contracts/CrowdsaleToken.sol#L102
Rebranded tokens include Ethos (ex. Bitquence) and ixLedger (Ex. InsureX). Some background https://www.ethos.io/2017/11/20/why-ethos/
Then the disclaimer: There is no ERC standard event for token branding information change. In practice wallets, exchanges and even some blockchain explorers do no read this information. You need to contact them one-by-one when you rename your token.