I suspect the answer, as is usually the case, will depend partly on your users themselves and their preferences for keyboard input vs. mouse input.
Atlassian suite (e.g., Jira) has a process sort of like your Example 1 flow, but with some important enhancements. First, when you start typing a name, a suggestion box will appear below the field to help you quickly get the user you're looking for. Second, you can autocomplete the user's name with the highlighted (top) choice in the suggestion box via keyboard or mouse action. Third, this autocompletion or selection action adds a bubble to the field with that username in it, adding the user to the list of selected users, kind of like in an email client. You can then immediately start typing another username to add a second user and repeat the process until you have selected all desired users. After that, you can Apply or Save in the modal to apply the action.
Benefits to a system like this:
- easy to quickly add a small-to-medium number of well-known users from a large volume of options via keyboard.
- autocomplete means fewer keystrokes and fewer input errors
Drawbacks to a system like this:
- no clear mouse-first workflow (though in Jira, I believe the most-selected users immediately populate the suggestion box on clicking the empty user selection field)
- time-consuming or potentially frustrating to select a large number of users (e.g., more than 10)
- difficult to add users whose names are less well-known to the user, or to use the list itself to enhance the user's mental model for making the decision about who to select
A potential hybrid solution would add a (+) icon to the right edge of the field which would display a modal with a list of usernames with checkboxes. This would address most of the drawbacks listed above with little impact on the interface for those who prefer the keyboard mode of operation. It should also present a reasonably familiar model to users who are used to email clients which provide a similar model (e.g., Outlook).
Actually, tl;dr: just use a model like Outlook where you can type to completion, type for autocomplete selection, or click to add users through a model with a comprehensive listing.