Hi Andrea Boa Hartwig,
We recently updated how you change participant names in Dovetail. To change a participant name, you just need to type in their name in the "Search and assign" text box and either assign them to an existing contact or create a new contact. If you are finding that the text box is greyed out/ disabled for you, it might be because your workspace has only given access to the contact database to Managers.
To check if this is the case and to update it, a workspace admin will need to go to Settings → Security settings and check under "Who can view contacts" if it has been set to Managers only.