VPOP3 does not (by default) place any restrictions on which email addresses or domains you can send mail from. However, there may be external restrictions on which email addresses/domains you can send from. For instance, if you send mail through your ISP's mail server, they may only allow you to send mail from specific addresses, or the domain you send mail from may have a sender policy defined, such as SPF or DKIM which will restrict which computers can send from the domain.
If there are no appropriate restrictions in place, all you need to do is set up the relevant address in your email client as the sender email address.
If you will only be sending from that email address, then this is as simple as changing the account settings in the email client. However, if you will want to choose from several different addresses when sending mail then this can get more complicated, depending on your email client. Some email clients are more difficult to do this with than others, for instance, it is very easy to do it in Mozilla Thunderbird but considerably harder to do neatly in Microsoft Outlook.
To set up alternate sender email addresses in Thunderbird, simply go to Tools → Account Settings, choose the relevant account and press the 'Manage Identities' button. Press 'Add', and you can then create your alternate 'identity', including name, email address, signature, which folder you want sent messages to be stored in, etc.
In Outlook you can only have one email address associated with one account, so if you want to be able to send from multiple email addresses in Outlook, you must set up multiple accounts - which means you have to tell Outlook to collect mail from multiple places!
If you only want Outlook to collect from a single POP3/IMAP4 account, but be able to send mail from several different addresses, this becomes very burdensome, as you will get errors if you use duplicated entries (eg have it collecting twice from the same account), or you will have to set up multiple POP3 accounts on the VPOP3 server.
There is a (quite complicated) way you can tell Outlook to skip duplicated or dummy accounts when collecting mail, which is what you need to do if you are stuck with using Outlook for your mail and can't switch to a more flexible email client such as Thunderbird. See http://ask-leo.com/how_do_i_control_which_email_accounts_outlook_tries_to_download.html for instructions.
You can also send from any 'From' address in Outlook - see http://email.about.com/od/outlooktips/qt/How_to_Send_an_Email_with_Any_From_Address_in_Outlook.htm - however this requires you to type in the From address every time, which is not very easy for regular use.