I want to fly from Germany to Australia via Bangkok.

However as I want to make the stopover in Thailand upon my return, I want to know if I can leave part of my luggage at Suvarnabhumi for about one week.

Is there any company I can contact to pick up my luggage and keep it until I return?

You'd need to go through customs to exit with luggage, in transit you don't do that, often luggage is checked right through

https://thai-rest.com/luggage-storage-at-bangkok-airport-prices-and-rules/

 

You can store luggage with this bunch, I've done it myself.

As @scubascuba3 says you have to clear customs, pick up your luggage and drop it off yourself, they can't pick it up for you

Upon exiting past Immigration and custom control area, move towards I think exit 4 and look to your right just behind the escalators to go down to taxi there is luggage collection booth

If  after exiting Customs, you go to the meeting point at Gate 4 and look back to the Boots Pharmacy there is a luggage storage service to the right of Boots and that is where to store your stuff.

I have not used the left luggage service at Suvarnabhumi but have heard its very good service

I understand that he is going straight from Germany to Australia.

Two separate flight tickets would be needed...

Correct.. There is NO way for YOU to remain airside AND also have one or more of your CHECKED baggage exit the airport and be given to a 3rd party while you continue onward as a transit passenger.

 

You would have to formally enter Thailand (that is clear Immigration) and reclaim said baggage and clear it thru thai customs.

 

Only CARGO can be cleared for entry without an associated passenger as cargo moves independently of an actual ticketed/traveling passenger and is processed inbound by customs quite differently than passenger baggage would be.