This question is in reference to Atlassian Documentation: Add data to users for advanced functions - JIRA applications only
Is it possible to require a new user to provide more information on signing up for a new account, e.g. telephone number?
No. Although JIRA supports some key-value pair stuff, only administrators can set it. There's no storage for other data, and there's no interface for any of it in the Atlassian stack.
You'll need to find/write addons to provide data storage and an interface on to it.
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