the size of /home reduced 3G but I can't found the name of new partition
Why should there be a new partition? Let's step through what you did:
e2fsck -f /dev/sda2
The partition is unmounted and checked.
resize2fs /dev/sda2 3G
The partition is resized. I don't do this very often but it seems bizarre to me that sda2 is now 5.0 GB, and not 3.0 GB, if that is what you asked for.
So you now have some free space on the drive that can be used to create new partitions. However, you did not actually do anything to create them, so of course they are not there.
To create a new partition without a GUI, use
parted (notice, no
g). IMO the former is simpler, although if you have a GPT disk, make sure your version of fdisk supports GPT (it will indicate if it doesn't). Note that as per
The resize2fs program does not manipulate the size of partitions. [...] If you wish to shrink an ext2 partition, first use resize2fs to
shrink the size of filesystem. Then
you may use fdisk(8) to shrink the size of the partition. When shrinking the size of the partition,
make sure you do not make it smaller than the new size of the ext2 filesystem!
I highlighted the first sentence to emphasize the fact that you have shrunk the filesystem, not the partition. This is a bit confusing since
df refers to device nodes (i.e., disk partitions) as filesystems. It actually refers to the filesystem on the partition, which is not the same thing.
So, now you have shrunk the filesystem, you can shrink the partition, then you can add a new one (and create a new filesystem in it).