Your display name can be added in Settings -> Account.
Prior to setting a display name, your email address is automatically used as a display name in most email clients. If your email address is email@example.com, your display name will be shown to the recipient of the mail as sarahw.
Below you can see what the email address firstname.lastname@example.org displays as when there is no Display Name set:
How the message will appear in Gmail (notice the far left displays “contact” as the display name):
Upon saving a Display Name, your messages will appear under a different name when received by the recipient.
Below you can see what happens when we change the display name for email@example.com to ProtonMail.
Releasing the Custom Domains feature, we also added a possibility to add/create different Display Names for each alias. To learn more about this, please visit this link: https://protonmail.com/support/knowledge-base/display-name-aliases/