Change sender name in Mail

The Name you chose for your Apple ID will determine the Name that will appear in your Apple Mail as Sender.

At least that how it works on all 3 Apple Computers and iPhone that I use

The name P. Phillips appearing on these Forums is also my Apple ID Name in My Apple ID

This is determined by your account settings at the server.

For example, to change the name that appears when I use my gmail account, I had to login to gmail using the browser, click on the settings icon, and change it there, and it was immediately taken up by Mail.

Probably the same applies with other types of accounts. Change the settings at the server.

You will have to get a new email account, like at Gmail.com, that is A & B@Gmail.com and use it.

You are allowed to have 3 aliases to an Apple iCloud email account. You will have to do that at iCloud.com at Mail's Preferences.

The following text is from the Learn more link in this screenshot:

Create an email alias

In Mail on iCloud.com, click  at the top of the Mailboxes list, then choose Preferences.

Click Accounts, then click “Add an alias.”

Provide the requested information:

Alias: The text you provide becomes the email address (alias@icloud.com). An alias must contain between 3 and 20 characters.

Full Name: The name you provide appears in the From field of the messages you send.

Label: Aliases are listed alphabetically by label.

Click Add, then click Done.

Change the full name or label

You can change the full name for an alias or a custom domain address. You can change the label for an alias.

In Mail on iCloud.com, click  at the top of the Mailboxes list, then choose Preferences.

Click Accounts, then select an address in the list.

Edit the full name or label, then click Done.

Turn off, turn on, or delete an alias

You can turn an email alias on or off at any time. You can also delete email aliases that you no longer want to use. While turning off an email alias is temporary, deleting it is permanent. When an alias is turned off or deleted, email sent to that alias is returned to the sender.

In Mail on iCloud.com, click  at the top of the Mailboxes list, then choose Preferences.

Click Accounts, select an iCloud Mail alias in the list, then do any of the following:

Turn off an alias: Select “Disable alias.”

Turn on an alias: Deselect “Disable alias.”

Delete an alias: Click “Delete alias,” then click Delete.

Click Done.

Note: You can’t delete or turn off a primary iCloud Mail address. You can’t use an alias to create a separate Apple ID, and an email alias can’t be converted to a primary iCloud Mail address.

So if you don't have more than 2 aliases already you can create a new one for A & B@iCloud.com.

Apparently, the issue is that iCloud - even though it allows more than one first name - only displays the first first name and the last name.

Here is a suggestion: why don't you edit the first name, using an underscore - say, instead of "Jack Jill", make it "Jack_Jill".

You are welcome and thank you too 🇨🇦

Do come back to the Apple Support Communities ( ASC )  in the future, if / or when additional questions may arise