Here's the configuration you should use for Namecheap Private Mail.
Email Provider: Other
SMTP Settings:
SMTP Username: {{your full email address}}
SMTP Password: {{your password to login}}
SMTP Host: mail.privateemail.com
SMTP Port: 465
TLS: TRUE/YES
IMAP Settings:
IMAP Username: {{your full email address}}
IMAP Password: {{your password to login}}
IMAP Host: mail.privateemail.com
IMAP Port: 993
TLS: TRUE/YES
To learn more about this connection you can visit NameCheap's Settings page.