How should one describe a future academic appointment

I would not worry about the title as much as the new location. Assuming a name badge that looks something like

Strongbad

PhD Student

Crazy Go Nuts University

I would add a hand written line to make it

Strongbad

PhD Student

Crazy Go Nuts University

Krusty's Clown College (starting August)

I would only do this if the contract has been signed and there is no contingency on you finishing your PhD. If you have to finish your PhD to start the assistant professor position, then there is no guarantee you will be starting in August.

Sorry to be a bit of a party pooper, but I don't like either StrongBad's or paul garrett's suggestions. Notwithstanding the fact that you deserve all the respect and congratulations in the world for your new near-future position, and it's very understandable that you want everyone to know about it, I can't help thinking that writing anything other than your current affiliation on your badge or presentation slides risks leaving a rather negative impression of someone who is a bit too over-eager to take credit for things that they have not yet completely accomplished. After all, you are not technically a PhD yet, let alone an assistant professor.

My advice is therefore to tell anyone you feel should know about your new position in private conversation, and wait patiently until the effective date of your new appointment before listing it on any official documents such as your CV or conference badges. This is a special case of my more general philosophy that one should never brag about achievements that one has not yet fully accomplished.