Hi,
unfortunately this is not possible natively anyway there is workaround.
- Create a field of type HTML delimiter with alias "firstname_display" and in description put a code like this

{user firstname displayed raw}

, set this field to be not available in profile/edit profile/registration form
- Create a field of type HTML delimiter with alias "artisticname_display" and in description put a code like this

{user artistic_name displayed raw}

, set this field to be not available in profile/edit profile/registration form
- Set following conditions in field "artistic_name":
1) if equal to custom value empty (leave empty custom value parameter) then show field "artisticname_display" (inverse Yes)
2) if equal to custom value empty (leave empty custom value parameter) then hide field "firstname_display" (inverse Yes)
- In Easy Profile options set display format name like this

{firstname_display}{artisticname_display}

Basically the field name is composed by HTML delimiter field type, but these fields are available only in according with conditions of "artistic_name" field.

Doc:
- Content plugin is used to show in HTML delimiter fields the value from other fields: http://docs.easy-profile.com/index.php/article/content-plugin

Thank you so much!

The only modification I made was inverting the conditions in field "artistic_name":

1) if equal to custom value empty (leave empty custom value parameter) then hide field "artisticname_display" (inverse Yes)
2) if equal to custom value empty (leave empty custom value parameter) then show field "firstname_display" (inverse Yes)

And it's working like a charm.

Now I just need to learn how to apply this to other components.