This page will help helps you configure the mappings to allow Connector for Salesforce & Jira to to assign a different user to a created issue.
Guide
Go to Settings > Apps, and then in the sidebar, under Connector for Salesforce, choose Bindings.
Choose your desired Bindings, then click Mapping.
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On the Mapping Configuration screen, choose the Issue Type you
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want to configure.
For this example, let's choose Task.
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Click Mappings.
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The Task to Case field mappings dialog box appears.
In the Jira Field, choose Reporter, and in the Salesforce Field, choose Owner ID.
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Click + Add.
Once you've clicked the + Add button, click on Map Values.
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In Reporter field, add the username of the account you want to add.
For the Salesforce Fields Value, you are required to obtain an 18-character Owner ID.
To get this, write down your 15-character User ID from your Salesforce profile URL:
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Use this tool to make the conversion of the User ID.
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Copy the converted ID, paste it under the Owner ID column, click + Add, then click Save.
Warning Make sure you paste or key in the Salesforce ID exactly as generated, with the correct case (this ID is case-sensitive). and with no spaces before or after the value. For example, 00590002fBnyAAEis not the same as00590002fbnyaae.
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In Salesforce, create a new case assigned to the designated owner, where the Owner in Salesforce is using the admin username that has already been mapped in Jira.
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Back in Jira, you should now be able to see the admin user instead of "Salesforce & Jira Cloud Connector" as the Reporter.
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Go to Salesforce and change the Case Owner to change the case's owner to ensure the add-on can synchronize with the Reporter field
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Go back to Jira and Pull the updated changes made in Salesforce.
You should now be able to see the new changes.
The user must be manually mapped as well.