Take your Bitcoins out of Coinbase. Coinbase has been consistently unreliable in terms of their uptime and I'm not sure if you'd want to keep the coins in an unreliable service. Try exploring desktop wallets (Electrum, Bitcoin Core) and hardware wallets if you've large sums of Bitcoin. I know many would argue about 2FA on Coinbase but I don't think 2FA actually adds that much security when you're talking about malware attacks.

You would be better off holding your own bitcoin rather than trusting a company like Coinbase. A hardware wallet like Trezor is not very expensive and will keep your coins safe. There are other measures like using Tor and encrypting your wallet that can also add extra layers of security. You can decide what method of securing your funds is best for your situation but I would advise withdrawing from Coinbase if you own a non-trivial amount of BTC.

I think 80% of the members on this forum have already answered about the security against Coinbase.

So, it seems I don't need to answer any more questions about the OP, you can see below.

Topic: Is coinbase safe? and this app this app claim free bitcoin?

Topic: Coinbase is scammers..

Topic: Is Coinbase safe to store currency?

I hope what is conveyed by the community here can make you think carefully.

You are not safe with that exchange because there are so many claims of having issue to that Coinbase site.

Try to have your own Ledger nano to keep safe your bitcoin and be secured holding that coins of yours.

And please prevent your self from leaving your crypto assets in any exchange because that is not reliable way of investing.

Even with all these precautions, it is still a bad idea to use Coinbase. After all, you are using a centralized service and your account is nothing but a record in a database kept at a centralized location. Any malfunction in the database (and backups) and all users lose their money. Moreover, the moment user checks that 'Terms & Conditions' checkbox, he becomes liable to the tyranny of the website. Make a small stupid mistake and your account will get banned and you will lose your money.

Using a non-custodial wallet is far better than using Coinbase with maximum security.

Regardless of the money, if you have intentions of keeping it for a long time then Coinbase is not the best choice. Even if you activate 2FA, email or authenticator that doesn't make sense if a hacker gets in through their backdoor and steal their funds. Although Coinbase seems to have a strong security but for someone who's security worried and you don't own your keys there. There are free desktop wallets that you can choose which has been suggested like Electrum or Bitcoin Core.

the bigger problem with centralized services such as Coinbase as wallets is when they decide to randomly shut down accounts for whatever reason they see fit. and you have already agreed to their terms and given them permission to do such a thing even if you didn't read the ToS when you signed up. your money can evaporate just like that.

I used to call them the PayPal of crypto ( analogy doesn’t work so well anymore  ) because you’re right they will ban you for anything they see fit..their own “moral code”.

I have been banned before (bought allergy meds from a 100% legal online pharmacy) but they did let me remove my coins I had on there.  However I’ve got a buddy (a legendary/very knowledge member here) who’s coins got stolen when they locked his account. No reason for it or explanation at all.

OP- buy a Ledger or Trezor hardware wallet, but make sure to only buy directly from the companies and not eBay/Amazon etc

Well, it's anonymous as long as you don't really provide your info, you'd just be someone on the internet that owns an x amount of BTC on their exchange. Exchanges aren't the best when it comes to storing, but it's one of the easiest ones since you don't particularly have to buy/setup something. If you want a really secure way to store your coins, follow what others say about hardware wallets. They're basically the best way to store your coins since you're basically the one in control yourself, and not anyone else.

Well, the 2FA for Coinbase can provide additional security but, -- having a hardware wallet is still the best way to secure your bitcoins because you can have your own private key besides Coinbase is only good for trading which I suppose you are not doing yet. There are lots of hardware wallets that you can use and since you mentioned that you are new in the bitcoin world I may suggest Exodus or Electrum which both are not too complicated to use but if you want to use it also for desktop ^[AFAIK] Exodus is better. Price is wise for a hardware wallet I know Ledger Nano is the cheapest not exceeding $60 for the amount but of course you may still do some research on which hardware wallet can be the best and suitable for you.

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The Biggest list of a hardware wallet that made by @Ratimov ^{[ https://bt.irlbtc.com/view/5282364.0 ]}, will help you.