I like it better than Zclassic.  BitcoinZ doesn't exactly roll of the tongue either though, so it will have to be called something else in day-to-day usage. Since BTZ is available as a ticker symbol, and it's easy to use (like saying "ETC" instead of Ethereum Classic), that would be a good choice.

One alternative name I just thought of is "Z-Bitcoin." With this you could just call them "Z-bits" which I think is easy to say and is a really good name. You could also use symbols ZBT or BTZ with the z-bits name.

Just my 2 Z-satoshis