Scotty why do emails sent from our computer and this yyy@gmail.com address, show up as having come from zzz@gmail.com I can send from my phone with no problem, but computer says (in the "from" box) smtp.gmail.com:zzz1949? People often reply to that account rather than "ours"……….ms
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There are a couple things to consider here. First, make open mail preferences. Next, select icon labeled “composing”. Now check to be sure the “send new messages from:” tab is set to the choice you prefer. You can have it always send from the same address when creating new emails (although emails that are replies will go out as the original email address they were sent from unless you change it manually before sending). If you chose “account of selected mailbox” as your choice then you always need to be aware of which mailbox you are currently viewing in the left column of mail. If you have sleeked “inbox” and are viewing all of them, then any new outgoing email will be sent from the uppermost account of all your inboxes.

A second thing to consider is to check which outgoing server your email accounts are all using. To do this go to settings once again and select the blue icon labeled “accounts”. Now for each account check the “outgoing mail server. You don’t want to use an ATT server for a gmail account, or a gmail server for an iCloud account and so on.

Last thing to check is that the email address is actually correct in the “email address” field within the same window.

Hope this helps.
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update:
Thanks Scotty; very helpful info. I checked and rechecked and everything in the aforementioned boxes appears correct. When I go to send something from the “name”removed account, the first "from" box says nameremoved@gmail.com, but the box to the right of that one says"smtp.gmail.com:nameromoved. When I try the scroll down bar to change, it says the (correct, I think?) "smtp.gmail.com:zzz” is offline. Any help will be appreciated, but I realize you've already gone above and beyond.
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Try going to mail preferences again. Go to the accounts tab and select the problematic email account in the left column. Under “outgoing mail server (smtp) select “edit smtp server list”. Once at that window, find the click the plus sign. Enter the following:

Next go to the advanced tab and enter the following:



Hit ok then go back to the account tab. Now under “outgoing mail server” select the new gmail outgoing choice.

Be sure to check “Use only this server”. If that doesn’t fix it, just delete the entire account and re-add it.