That's good...
In the same theme, Rental as Anything
Rental as Anything is very good. I like it, especially if you're pitching at the inner 2-5 km rim, say Richmond, Fitzroy, Carlton, Brunswick, Northcote, Footscray, etc. It is quirky and catchy.
I am assuming that the establishment of this business will not be a "one-off" office, but rather the first of many expansions. If it is the former, nothing wrong with using your name and branding the PM and sales (or BA) side of the business as is the custom....using first and last names or just your last name. That assumes you will only be in one location/precinct.
Assuming you wish to roll-out several of these after a while, keep the name you choose generic. Branding, as you have come to realise, is very important.
Here's a couple you may consider:
Rent Smart
Smart Rent
Rent Easy (eezee)
Easy (eezee) Rent.
You need to keep it neutral from the perspective of both landlord and tenant. Both are your customers, so making the name/brand too landlord friendly to appeal to listings on your rent roll may be off-putting to the tenant for example.
Whatever you choose, run through the ASIC register and name search and establish your trading entity.
Have a read of the E-Myth by Michael Gerber if you haven't already. I know you are ambitious and have the fortitude and "go get 'em" attitude, so set this up right from the start as if you were setting up a franchise (system) to sell.
I have premises for you in Brunswick East if you wish