I'd say NO. Obviously god isn't concerned with his name because he's kept it hidden. Jesus didn't mention it...... come to think of it there's lots of stuff Jesus didn't mention that the WT promotes.
It was a bad idea to call themselves Jehovah's Witnesses, their desire to be different has always tripped them up. They should have stuck with International Bible Students or even better....... Christian Witnesses, something with a little dignity.
When JW's say 'Jehovah God', that tells me they have no real confidence that people understand who jehovah really is since it's not a name most people think about or use. Tacking god on to it is well....tacky
People don't say Allah God, or Baal God, or Thor God do they?
I also sense that ex witnesses who refer to god as jehovah sound like they are still transitioning out of WT dogma.