You can create a new issuetype named "Requirement" and create custom fields, screens, workflow etc for it. Everything else will be similar to Tasks and Bugs.
You can create different issue types in Jira, but if you mean having another object like 'Issues' but with a different name, I don't believe it's possible.
To create different type of issue you can check this documentation:
https://confluence.atlassian.com/display/JIRA/Defining+'Issue+Type'+Field+Values
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The link is nearly 5 years old, things have moved on. Have a look at the current docs for your version of Jira.
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could you explain little more brief?
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