Multiple VGs found with the same name: skipping ** Use the VG UUID with --select vg_uuid=<uuid>
This would give the same result if you are trying to rename a LV that has a name that belongs to two Volume Groups. At these cases, you only have the option to use UUID. blkid command doesn't give the UUID of the volumegroup. To find the volumegroup UUID, you would need to use vgdisplay. Once you have the UUID for the desired VG, it turns out that you can use the vgrename directly only UUID like the following:
vgrename hL1QTc-gS2a-2xHR-XU1F-Of9Q-sgUQ-ckMxkF vg1
This would rename volume group with UUID 'hL1QTc-gS2a-2xHR-XU1F-Of9Q-sgUQ-ckMxkF' to vg1 regardless of it's previous name.