How can you keep your email address when you change internet service providers?

Not likely, if the email address was provided by your previous ISP (internet Service Provider). Because that email account is included in the package of benefits for paying customers. But yes, if the email address is available to anyone, such as webmail (Yahoo, Hotmail, Gmail, etc.), or an unrelated POP or POP-compatible email (GMX.net, Inbox.lv, Aim.com, etc., etc.).