Sorry for delay with reply...
Are you sure that you have at least 3.2.0 QaSpace version?
The matter is that we have released this piece of functionality in 3.2.0 version.
Please download it from here for free https://marketplace.atlassian.com/download/plugins/com.epam.jira.tm.test_management/version/2000082
But pay attention that it's supported only JIRA 7.
So you won't be able to intall it until you upgrade you JIRA instance to any 7.X.X version.
Hi! Please make sure that you try to get
Dear friend, it's possible not to show project name in QaSpace project chooser. But it requires manual removing our custom test issue from each project's issue type scheme. Any time you will need it again - you are able press Unable QaSpace button inside a project Administration page.
I hope it helped you.