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Are they all using the same wireless/network?<br />
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If the non-domain computers are connected to different wireless that is outside the network then you may need to create an A record that points mail.company.com to the internal IP of your mail server.<br />
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It is probably struggling to resolve the name internally.<br />
<br />
You can also setup the Outlook Anywhere settings even if you are using a domain account under the proxy settings inside the advanced settings when setting up the account.
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Are they all using the same wireless/network?

If the non-domain computers are connected to different wireless that is outside the network then you may need to create an A record that points mail.company.com to the internal IP of your mail server.

It is probably struggling to resolve the name internally.

You can also setup the Outlook Anywhere settings even if you are using a domain account under the proxy settings inside the advanced settings when setting up the account.

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I have a few AD users that don't have a need for their own primary Exchange mailbox. &nbsp;They all currently log into Webmail and use the same one, support@domain.com. &nbsp;In addition, some users connect via their local NON-domain computer with outlook (HTTPS\RPC) and it works fine. <br />
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The issue i have is when attempting to connect outlook on a domain enabled computer to this &quot;shared&quot; exchange account I receive the following error:<br />
<br />
&quot;the name cannot be resolved. the name cannot be matched to a name in the address list&quot;<br />
<br />
Why would outlook give this error on a domain pc, but a non-domain works great.
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I have a few AD users that don't have a need for their own primary Exchange mailbox.  They all currently log into Webmail and use the same one, support@domain.com.  In addition, some users connect via their local NON-domain computer with outlook (HTTPS\RPC) and it works fine. 

The issue i have is when attempting to connect outlook on a domain enabled computer to this "shared" exchange account I receive the following error:

"the name cannot be resolved. the name cannot be matched to a name in the address list"

Why would outlook give this error on a domain pc, but a non-domain works great.

Outlook on Domain computer cannot connect to other shared Exchange Mailbox

Microsoft Outlook is a personal information manager from Microsoft, available as a part of the Microsoft Office suite. Although often used mainly as an email application, it also includes a calendar, task manager, contact manager, note-taker, journal, and web browser.

Outlook

Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.

Exchange

An email client, email reader or more formally mail user agent (MUA) is a computer program in the category of groupware environments used to access and manage a user's email. A web application that provides message management, composition, and reception functions may internally act as an email client; as a whole, it is commonly referred to as webmail. Likewise, email client may be referred to a piece of computer hardware or software whose primary or most visible role is to work as an email client. Email clients can also have other systems, like calendars, notes and contact managers.