Yes electrum wallet, blue wallets can change your bitcoin address to a new one for you to use to receive your bitcoin, and the new address which you are using to receive bitcoin will reflect on the blockchain. Bitcoin blockchain is transparent and every address with bitcoin in it will be on the blockchain because that's where your bitcoin is stored. It's just like a bank. Your cash is stored in the bank and you can use your atm card or cash book to send money to another account which the money must reflect in the account.

But would it be traced, the funds that got onto the new address, so to speak?

Thanks, I think I've slipped that detail out, I just never did such a process myself - and if it's done automatically (the funds just go to a newly created address, the previous one is drained, perhaps), how one may even try to hide the tracks..

The wallet owner can totally move their coins to a new address but the bitcoin blockchain will still keep a record of it. You'll see the coings going from the old address to the new one, it's all out there. Even though they can choose where to send the money, there's no way to completely hide the history since bitcoin is all about being open like that. You can try special wallets to make it more private but the first transaction will still show up

Every transaction will always be present on the blockchain. The only way to hide the transaction is if you used a mixer service so your transaction will be mixed in with other transactions to only show as one transaction on the blockchain.
The wallet can’t just change the address that’s already on the blockchain but the wallet can generate a new address.

If you are carelessly shared things on Internet, it will be there forever and your privacy lost forever and can not be resumed.

It is impossible because you missed an important point about Bitcoin blockchain. It is a public blockchain, not a private blockchain and all transactions are publicly and traceable by everyone.

This explains why hackers in famous cases will be caught when they moved stolen bitcoin in known addresses to a centralized exchange. Their stolen bitcoin will be frozen by exchange and wait for further action from governments.

If you care about privacy, read many documents on it in Bitcoin Privacy Guides.

I don't fully understand your question. If you send your funds to the new address, your bitcoin will be in the new address on the blockchain. However, you can still use your old address will still be valid and bitcoin can be sent to your old address. Bitcoin wallwt address does not expire but it's good not to reuse one same address to receive bitcoin.

Yes, old wallet addresses can still be used.  For example, I have two wallet addresses on my profile.  If you look them up, you will notice they have received a couple transactions both during my time on this forum.  I can spend from it as many times as I want.  The reason your old address is 'changing' is because it is a good practice for your privacy.

My privacy situation is really bad.  I am PrivacyG, I shared a set of two addresses and I received a ton of transactions to them.  They are all linked to one address, meaning they are all mine with zero doubts and everybody looking up my address knows it.

The reason I do not care is because it would be really hard to change the address linked to my forum account every single time I had to receive a payment.  It would not only be significantly more complicated but in my opinion a waste of time.  I could change my address 100 times, it will still show up particularly under the 'PrivacyG' username.

But privately, I am using new addresses every time.  This is because things are harder to supervise that way by a third party.  Although there are now Blockchain Analysis companies doing particularly this and trying to put together all our transactions to link them to identities, it is still a better practice than re using the same address over and over again.  It is a complicated subject and I could write an entire book about it, but to shorten the length of the story this is simply a very good privacy practice.

When it comes to transaction on blockchain, it must be recorded on the ledger but there are some wallets that can change wallets for instance, the transaction would not show the exact destination but  it is recorded on chain and wallets that does such is electrum, blue wallet just like the some members had mentioned here. Another thing is that if you do a transaction with the above mentioned wallets and there are still balance left on it, when you check that same wallet, you would see the coin but when you change the wallet through the explorer, you would not see anything there but the coin is still there. that has been my experience with the wallet.

I don't know whether you are new here or you are new to Bitcoin wallet and how it works.

As far as I know the question you ask is public and often submitted by beginners, yes is common, embarrassed to ask heretics on the road, maybe you are lazy to find topics like this:
1. Topic: Electrum and change addresses
2. Topic: HD wallets and change addresses
3. Topic: Paper wallets and change addresses. Please help me understand a warning

And many other topics, that's an example.

However, you don't need to worry about it, you will find the answer in detail below, I hope to help you as a whole.

Please read: Can the cryptocurrency address linked to a wallet be changed? If so, what is the process for changing it?