Your request is extremely confusing to me. The “Dsname Level” that appears on the screen when you start the ISPF Data Set List Utility is only a data set name if that was what you specified the last time you started the data set list utility, otherwise known as ISPF 3.4. It is only a data set if that what was specified the last time you used data set list.
For example, right now, in my TSO session, I see userid.xxx. What it actually is is none of your business. I press my Enter key and ISPF displays a list of data sets that start with userid.xxx. I go down to, for example, userid.xxx.SYSPRINT, enter B is the command column to the left of userid.xxx.SYSPRINT, and press my Enter key, and ISPF will “browse” userid.xxx.SYSPRINT. If I then press my End key, usually the F3 key, ISPF will return to the data set list. If I press the End key again, ISPF will return to the primary menu for ISPF Data Set List, and ISPF will again show userid.xxx, not userid.xxx.SYSPRINT. ISPF retrieves userid.xxx from its “profile,” which you did mention, not userid.xxx.SYSPRINT, the last data set I “browsed.”