Is there a way to find the volume group name after assigning hdisk to the machine for importing it ?

importvg -y <find_the_name_from_the_unknown_disk_> hdiskX

The VG name is stored in the ODM, not on a disk. On the disk is only the VGDA which has the VGID stored.

You can use the following to read the VGDA before importing it:

lqueryvg -tcAp <hdisk>

Thanks Zaxxon for the reminder.

Sometimes importing a volume group, which has same Logical volume names would rename it by itself. To avoid renaming of the logical volumes, is it possible to know the contents ( logical volumes + filesystems + volume group name ) before importing.

The reminder vanishes in a month.

When the LVs already exist, you will always have to rename them, either by the automatic mechanism you described or by yourself manually before doing the import.
Anyway, you should be able to read the LV names the way I have described before the import.

If it is a cluster, VG names and LV names have to be unique in the whole cluster. If it is a kind of rescue import, maybe choose some test box to avoid a mess up of names.

If you can get the ODM files from a restore of the box where this PV/VG originally belonged too, you could get it from there by examining the ODM files.