I'm having weird issues with my internal Fusion Drive.

Symptoms:

1. It gave itself a new cryptical name, and I can't change it back
2. In most cases I cannot install new software anymore (e.g. I cannot update Flash)
3. It is sometimes shutting down immediately
4. Disk Utility says "no errors found" but can't mount it.

See below for some screenshots:

Referring to Point 4 and 1 (says: Volume seems to be ok, see the weird name...)

Referring to Point 2 (says: Installation failed)

Error while mounting Flash Player installer image:

26.11.15 10:03:42,000 kernel[0]: hfs: mounted Adobe Flash Player Installer on device disk3s1
26.11.15 10:03:42,082 mds[55]: (Volume.Normal:2464) volume:0x7fb9ef004600 ********** Bootstrapped Creating a default store:1 SpotLoc:(null) SpotVerLoc:(null) occlude:0 /Volumes/Adobe Flash Player Installer
26.11.15 10:03:53,137 authexec[510]: executing /Volumes/Adobe Flash Player Installer/Install Adobe Flash Player.app/Contents/MacOS/Install Adobe Flash Player
26.11.15 10:04:14,000 kernel[0]: hfs: could not initialize summary table for Flash Player
26.11.15 10:04:14,000 kernel[0]: hfs: mounted Flash Player on device disk4s2
26.11.15 10:04:17,000 kernel[0]: hfs: unmount initiated on Flash Player on device disk4s2

diskutil cs listoutput from Terminal:

CoreStorage logical volume groups (1 found)
|
+-- Logical Volume Group BD4DE488-7C63-4FBA-9FAC-9B92CD56EDE4
=========================================================
Name:         FusionDrive
Status:       Online
Size:         1249060388864 B (1.2 TB)
Free Space:   0 B (0 B)
|
+-< Physical Volume C106FB79-47F5-4967-924F-043C553FC58E
|   ----------------------------------------------------
|   Index:    0
|   Disk:     disk0s2
|   Status:   Online
|   Size:     249715376128 B (249.7 GB)
|
+-< Physical Volume 6492048E-B397-4457-A12B-DA62DD379B35
|   ----------------------------------------------------
|   Index:    1
|   Disk:     disk1s2
|   Status:   Online
|   Size:     999345012736 B (999.3 GB)
|
+-> Logical Volume Family 40A9F389-D3F0-4D75-89A3-36FFAEA6FD57
    ----------------------------------------------------------
    Encryption Status:       Unlocked
    Encryption Type:         None
    Conversion Status:       NoConversion
    Conversion Direction:    -none-
    Has Encrypted Extents:   No
    Fully Secure:            No
    Passphrase Required:     No
    |
    +-> Logical Volume E02059A8-E5D4-4DFF-9D0F-49408380838E
        ---------------------------------------------------
        Disk:                  disk2
        Status:                Online
        Size (Total):          1242500358144 B (1.2 TB)
        Conversion Progress:   -none-
        Revertible:            No
        LV Name:               ´+ßPÜÜÜÜÜPÜ09O8UI9OOOOOOOIOO09O987UUUUZU6T786Z65444RRRR3ERR5EREREREER5R4E43E4ED43ERE3434R43RE3ER4E3R45REW4W45W343E43W424323231QWQ3W3W23432123432323E23E21W23453213E43212R2WEW1221QQ^21
        Content Hint:          Apple_HFS

output from Terminal for command sudo gpt -r show /dev/disk0

     start       size  index  contents
         0          1         PMBR
         1          1         Pri GPT header
         2         32         Pri GPT table
        34          6         
        40     409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
    409640  487725344      2  GPT part - 53746F72-6167-11AA-AA11-00306543ECAC
 488134984     262144      3  GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC
 488397128          7         
 488397135         32         Sec GPT table
 488397167          1         Sec GPT header

My counteractions so far

1. Ran the Apple Hardware Test. Result: nothing found.
2. Ran the First Aid (see screenshot). Result: nothing found.

No backup is available.

Any help is much appreciated! Wanna get rid of this :(