How can I change the passwords in Apple Mail?

Usual reason is that the Mail account does not match the TalkTalk requirements.

Or as has happened with various providers, the mail servers are sometimes offline.

General info on mail troubleshooting:

Troubleshoot email problems in Mail on Mac - Apple Support

Using the Connection Doctor tool to see more of what's happening:

Use Mail Connection Doctor - Apple Support

Start with the Connection Doctor, and see what it reports. If that's not clear, post the diagnostics here, and somebody can work through with what's been found.

Oh, and there are TWO sets of server settings with two sets of access credentials and server settings for each mail account. One set for receiving and reading mail via POP or IMAP, and the second and separate set of credentials for sending mail via SMTP or ESMTP. Both sets of credentials have to be correct, or mail won't work correctly.

As has happened, folks reset one set of credentials or one password, and don't realize that the error message they're (still) seeing is referring to the other set of credentials. (The SMTP or ESMTP server settings and server credentials are accessed via the "Edit SMTP Server List" popup for the Outgoing Mail Account selector in High Sierra, so not easy to find.)

This discussion is definitely not yet to this point, but... And if all else fails, have complete backups of your environment using Time Machine or other tools onto external storage—POP accounts and messages are usually downloaded and stored locally on the Mac and not on the mail server, and deleting the POP account clobbers the local store—and delete and re-add your account. The backups will preserve your existing messages for recovery.

Hello,

Open Keychain Access in Utilities, then either check the Password under that item, change it, or delete it and start over.

Enter the part after the @sign in the search bar.

You may have duplicate or more entries in Keychain Access.

If using a browser to login via WebMail works it's not Name or Password, but likely old passwords interfering.

Shortest answer:

You do not have correct settings. You are not unique here, you are certainly not going to get help from an ISP as they’re next to useless in this regard, and you’re either heading toward deeper understanding of mail and mail authenticarion and sertings, or toward enlisting some (trusted) help knowledgeable in mail and mail authentication and secondarily in the macOS mail client. The local Apple Store, or Apple Support, maybe.

Passwords and reset protocols:

Remembering passwords and not losing our tokens is where we are. Which means using keychain or another password manager, and dealing with contacting support folks when passwords are lost or forgotten or re-used or otherwise exposed. And part of that is getting the credentials entered, and getting the correct server sertings entered in the case of mail, for both sets of credentials associated wih the connection.

Long answer:

Implementing a “forgotten password” protocol would involve modifications to a large chunk of the Internet; to mail servers and to each of the ISP authentication implementations, and to whatever 2-factor authentication scheme and whatever lost-token-card scheme or other two-factor or multi-factor scheme that an increasing number of folks are using to,secure access, and modifications to whatever each might use for authentication.

The design of that reset protocol is also going to a whole lot of discussions and a whole lot of stakeholders debating and then a whole lot of coding and testing, and then software upgrades, and across a whole lot of very different computer systems.

Because no client is going to want three or four reset protocols, much less thousands or millions of unique and mail-provider-specific reset schemes.

And a whole lot of revewers and testing folks and the usual sorts of nefarious folks and narional,security entities then try to spoof or break the new password reset scheme.

Not a small project.

Whatever authentication scheme is chosen here will still be subjected to folks lying and scamming to gain access to your email accounts, or to your phone numbers, too.

Here? What to do with a forgotten mail password? Contact the ISP and authenticate with them and then ask them to change the password, if they don’t provide web access and a reset mechanism; a fall-back contact email address or additional security questions or a phone number or a token card, or whatever the particular ISP has chosen for secondary authentication. Then reset the password in the read/receive path (POP or IMAP) and then in the sending path (SMTP or ESMTP).

Here? What to do with all the passwords we’re accumulating? Use a password manager. There are add-ons for various configurations, and Apple provides Keychain with macOS and iOS. Other operating systems usually have password managers, though not all do. Use the password manager to store the password. Or in the case of Keychain and some others, use the keychain to store secure and encrypted notes to yourself, containing (small) amounts of sensitive information.

And there are folks debating what to do with those that have died, and their passwords, and folks that are no longer legally competent to maintain passwords, what happens with warrants and government access and how that might work (and without defeating all client security) and how to maintain secondary authentication for recovery without opening up customers to social engineering (scams and cons, whether directed at the users or at the companies and their agents in control of the passwords), etc.

BTW...

There’s a booming business—business, as there’s lots of money to be had—in using password data from server breaches being used to try to breach other servers. To use credentials from one site to try to access others. This is really popular among the scammers right now, and this is why re-using passwords can be trouble. Not because you,forget your password, but because some server doesn’t store your password securely and doesn’t use a modern password hash, and that server than gets breadhed and exposes thousands or millions of usernames and passwords. And those then get tested everywhere else, against other services.

What happens with big Internet-wide projects?

We’ve been working on an Internet-wide upgrade to increase the available number of hosts—migrating the IP address space (to IPv6)—for ~twenty years, and we’re nowhere near done with that. These things can take decades.

A password reset scheme for mail—or more generally—can still be an interesting suggestion to make to Apple, though.

There are two sets of user and password credentials for each mail account present within Mail.app.

One set of credentials for sending mail (SMTP or ESMTP) and one for receiving mail (POP or IMAP).

Both user and password credentials must be set (separately) and correctly. Both have server and some other related settings.

The first set of login credentials is the obvious POP or IMAP credentials, and Mail.app makes it very easy to find these.

The second set of credentials is buried under the server settings and the Edit SMTP Server List selection in the pop-up, and the credentials for each specific SMTP or ESMTP server configured within Mail.app.

Both user and password must be correct in both places, as must be the TLS encrypted/secure connection settings, and the host name and port.

Additionally, TalkTalk requires TLS encrypted connections for POP and IMAP, though a number of the credentials-related postings around the 'net appear outdated and reference unencrypted connections.

Here are the TalkTalk settings...

Match these up with what you have, and in both places; on the POP or IMAP settings, and in the SMTP or ESMTP settings that are hidden away within Mail.app. In addition to the user and password credentials, you'll need to confirm that the port numbers, tge TLS encrypted/secure connection settings, and server host names are all correct.

As a troubleshooting tool, Connection Doctor can help determine what configuration errors might lurk:

Use Mail Connection Doctor - Apple Support