Hi Mariana,
Yes, it is possible to add custom fields such as user picker, text field etc in JIRA Service Desk.
To do so, please:
-create the custom field: https://confluence.atlassian.com/adminjiracloud/adding-editing-and-deleting-a-custom-field-776636410.html
-and then add it to the project screen and then add it to the Service Desk : https://confluence.atlassian.com/servicedeskcloud/configuring-request-types-and-workflows-732528910.html
Also, I would like you to check out list of supported custom fields in JIRA Service Desk] if you wish to customize more.
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