Partition numbers reported by tools are “immutable”, in the sense that there is no way to override the auto-assignment made by the disk partitionning tools.
Those numbers are assigned because of how the partitions were created, the logical structuring and sequencing of the process in creating them for, as Dennis indicated, for MSDOS partitioning [technically referred to as the MBR (Master Boot Record) partitioning method].
Not sure why you would want to “tamper” with those numbers, except to make them “look pretty” somewhere but there would be no benefit derived, functionally, by any re-numbering, IF such were to have been possible.
Tools to help understand where, physically, each partition is located (and implicitly why) are the following two commands (which can be tweaked to report in the fashion you desire).
The information offered below applies to GUID partitioned disks.
NOTE: The partition numbering for any partition table is based on the physical location of those partitions, and NOT based on the sequence in which they were created. If you insert a partition between two existing partitions (shrink the one closest to sector 0; reallocate the free space to a new sector), that inserted partition will be assigned the number after the shrunken partition, and all others after it will have their numbering incremented by 1. To demonstrate that, look for the label “DB001_F8”, which was the last partition created on the disk for which the partition list is provided below.
COMMAND: lsblk
sudo lsblk -P -p -o NAME,FSTYPE,PARTLABEL,UUID,MOUNTPOINT | awk '/[/]dev[/]sd[a-z][0-9]/ { print $0 }' | sort -V --key=1 | grep sda
giving you a report that looks like this:
For myself, I usually sort on key position 3, so that the outputs are sorted by assigned LABEL values, namely logically, rather than the “physical” label, which is the partition’s device name (sda?).
I would be curious to know if your “PARTLABEL=” values show the various sda[0-9]* identifiers by default, if you haven’t assigned them a specific LABEL string yourself. 
COMMAND: parted
sudo parted /dev/sda unit B print
giving you a report that looks like this:
Here, I report the start and end positions as B (Bytes) which, for me, makes it easier to calculate to the sizing such that partitions start or end on sector starts/ends, thereby ensuring partition “alignment” which ensures fastest data transfer for read/write.
COMMAND: fdisk
- WARNING: DO NOT ATTEMPT TO MODIFY GParted PARTITIONNED DISK WITH THIS COMMAND.
( used only to verify if partitions are properly aligned; when they are not, there is a report of the form “Partition # does not start on physical sector boundary.” )
sudo fdisk -l /dev/sda
giving you a report that looks like this:

Having learned from the experience of building my ROOT disk, I was then able to ensure my 2TB backup drive was properly partitioned such that all partitions were correctly aligned.
