Hi Mark (and to any members that may have a similar question).
Thanks so much for your reply. I'm glad it's unlikely that suppliers would avoid dealing me with me if I am a sole trader.
I have since called the Australian government authority (ASIC) regarding a transfer of my business name from my Pty Ltd company to a sole trader business and they said that I can also have the same business name for both of these entities. They said this would be considered/classified as a joint venture.
The above comments are based on my conversation with an ASIC representative. Anyone with a similar question should contact ASIC to check if this applies to their circumstances.