First thing, do not bring your wife and kids here until your training is done.
You will be putting your success in training at risk. Seriously, leave them
at home.
The names on all documents should match. She doesn't have to have your
last name, but the names need to match or else you run the risk of getting
screwed around.
Get the marriage certificate stamped by both your own government, and then
by the Qatar embassy in your own country before bringing it here.
Else you will have to do the same thing, but from Qatar, much more expensive
and time consuming.