(Even though df does show free space).
Most obvious cause is lack of free inodes.
Use $ df -i to see the amount of free inodes.
Each file takes one so if there's none free files will have to be deleted. Temporary directories, caches (~/.cache, ~/.thumbnails) and trash are good starting places.
Volume groups with the same name can't coexist. When a disk is enabled containing the same volume group as an already active group an error like this will be shown upong running vgscan:
WARNING: Duplicate VG name vg0: Existing abcD1e-fgHi-jklM-NOpQ-RSt2-UVwx-34YzAB (created here) takes precedence over BAzyxW-vU4T-S3rq-ponM-LkJI-hG2f-Edcb1a
Some of the vg* tools can take a volume group ID too, e.g. to rename the second group:
# vgrename BAzyxW-vU4T-S3rq-ponM-LkJI-hG2f-Edcb1a vg0_alt
References: https://bugzilla.redhat.com/show_bug.cgi?id=147361