The name is typically related to the reseller.. so in this instance although Boost = Telstra, the network name will be Wollies, as that's where you bought the resellers rebadged SIM from.
As for being slow.. that will depend on your distance to the exchange, line of sight and congestion on the cell tower.
I recently joined Boost and noticed that the network name on the mobile shows as "Woolworths" and I also noticed that the network is very slow.
That sounds like you are on a Woolworths Mobile service (which are a using different systems and the different Telstra Wholesale network). For Boost, it should appear as Telstra or Boost.
Maybe double check you have definately got a Boost sim card installed/activated.
Also, maybe try dialling #111#, and if you can access that see what it says under the option for "Offer".
* I am a Boost Australia customer. This is a peer to peer community where users help each other.