@Armin Cseve, what do you mean by "the name instead of the task's code"? Do you mean you want to see the issuetype name, e.g. "Task" or "Sub-Task" rather than the icon? If so this is not available natively. Unsure if there is any plugin that would allow this or not.
ok i think i see what you are asking for. You want all sub-tasks w/in the dasboard gadget to display the Summary field as parent Summary/child summary rather than parent IssueID/child summary.
This is not possible natively and unsure if there may be a plugin for this.
maybe i´ve got a solution.
If you use the filter statistic gadget in your dashboard, there is in the configuration under "columns to be displayed required" a column called "parent" (the designations differ depending on the language).
After that configuration you see the Full Name of the subtask instead of the key.
I hope this also solves your problem
Have a nice day