Do you know the user's username? I just did a quick test on my own JIRA instance and using description ~ "achristensen" pulled up all issues in which I was mentioned in the description. Using the display name of the user does not seem to work.
Re: having multiple ticket owners - have you considered using multiple user picker fields? By default, JIRA has a custom field type called "single user picker," so you could theoretically use several of those fields to tracker multiple owners, if you want. There's also a "multi-user picker" custom field type, so you could also list all of an issue's owners in one field. Watchers isn't a bad way to go, either, but I feel like Watchers serves a bit of a different purpose (i.e. someone who isn't going be involved in the completion of the issue, but needs to know what's going on, when it's resolved, etc.).
In my personal opinion, I think the design behind having only one Assignee is the way to go. If it's assigned to one person, there's no question as to who is the current person who is working on the issue. That said, I can see the situation in which you would want to maybe use a multi-user picker custom field to reference who might touch a ticket, but I think it's good practice to only have a single Assignee.
Hope this helps!
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