Is it Possible to store the user who resolving the ticket automatically in this custom field when user resolving the issue without entering manually?
You can either create a Jira Automation, or place a workflow PF when resolving the issue.
In jira automation you can create a rule:
For the workflow PF, you have to have an app like JMWE, which will allow you to write a short groovy code to get the current user to that specific user field
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