Hello @DeidreAnderson ,
If the names weren't uploaded to your account's contact dashboard, then you won't be able to search for them since that information wouldn't exist in the account to be searchable. If you have a separate database or a file with the names associated with the email addresses (contacts), then you can upload that to your dashboard, and it'll update those existing contacts' name fields. Make sure if you're doing this that the first and last names are in separately marked columns.
Beyond that, there's nothing else that can really be done. Generally speaking contacts need to provide you the information you need associated with their email address, it's not something that can (or should as a privacy concern) be found just by searching on the internet. If your contacts sign up through a form, I'd advise making sure you add a field to collect their first and last names, and make it required for submission if you're needing it for your communications. That way when they sign up, they can include that info.
Another possible option is to just make a simple landing page sign-up form through us, word it like it's a confirm / reconfirm information form, then include the form in an email sent out to your contacts. You could make the subject line of the email something like "Please Reconfirm Your Communication Preference" or "Please Confirm Your Contact Info."
Formatting contact files for import
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