Yes, that new address has a new private key... however, if you have an HD wallet (does it have the HD symbol in the bottom right corner or is it crossed out?) there is a chance that having one compromised private key could compromise your entire wallet (as all the private keys are "related" in a very complicated mathematical way)
If it is non-HD wallet (HD symbol crossed out) all the private keys are randomly generated and not related. The only "risk" comes from accidentally using that compromised privkey/address again in the future.
In my opinion, the safer option is to move to a new wallet... but moving all the coins to a new private key/address is definitely better than doing nothing.
Also, can I name the wallet.dat file anything I want or does it always have to have the .dat extension to work?
I believe that Bitcoin Core allows you to specify the wallet file at runtime using the
-wallet option, so theoretically you can name it whatever you want... wallet.dat is just what it defaults to if no wallet file is specified.
You might want to be careful renaming it... I've seen posts by several users on here that have previously done this and then been unable to remember/locate the file at a later date
Also can you please help me understand how to do a rescan of the blockchain within Bitcoin Core client?
to do a rescan... simply start it using:
path\to\Bitcoin\installdir\bitcoin-qt.exe -rescan
On windows... likely to be something like: C:\Program Files\Bitcoin\bitcoin-qt.exe -rescan
or add rescan=1 to the bitcoin.conf file in your Bitcoin data directory (where your wallet.dat is)... if you don't have a bitcoin.conf, just make one using a text editor. Just remember that once you have done the rescan, you should remove rescan option from your bitcoin.conf or it will do it EVERY time you start the program!
