Unless they've changed this, you can watch old episodes of BG you've missed courtesy of their website.
Frankly, my reaction is mixed. I understand and agree with their reasons, assuming you just can't trademark or successfully market "SciFi". On the other hand, I positively despise words or terms deliberately mispelled (there's a special place in Hell for those replacing plurals with 'z').
Syfy . . . ugh! My first impression is simply: ugh.
As for coming up with a better name, just off the top of my head: The Imagination Channel (or even ImagiNation); Quantum; Dimensions. That took 1 minute.
Likely they're all trademarked or owned. I suspect SyFy was selected because no one was dumb enough to want it or trademark it already.
As for animosity over canceled Stargate, mine stems from two far better shows (IMO) they axed: Firefly, and Farscape. Although the former's cancellation was more of Fox's ignorance than SciFi's.
Seriously, do they ever poll people, instead of "batten down the hatches, full steam ahead"? This is a bungle on the scale of New Coke!