Isn't the procedure that I would need insurance at the time of registering/putting the ownership in my name?
Technically, yes.
However, the penalty for not having insurance is not enforced at registration, but rather when you are stopped on the road by law enforcement.
Things may have changed since the last time I registered a vehicle at Service Ontario, but the clerk has never asked to see proof of insurance. There is a spot on the form to fill out a policy number. Once I bought a motorcycle in the winter, but didn't buy insurance till the spring, so I just put my car insurance policy # on there. No checks. Got the motorcycle registered, got a license plate.
My advice to you is to get everything as legal and straightforward as you can. Having different names and provinces on your ownership than what is on your license or passport is only going to cause you untold amounts of grief and headache when you need to deal with government officials in a foreign country.
You haven't mentioned which country you are going to, but from your description, I am assuming that it's not one of the more developed ones in Europe. If there is any corruption in that country, you are opening yourself up to having your vehicle held hostage by law enforcement or some government lackey looking for a bribe because your paperwork is irregular.
I have been on the receiving end of this, even when I had all my documents in order. I can't imagine if there were any discrepancies, how much time and money that would have cost me.
To answer your 1st question, the bike is going to stay in Europe. The container I have for free
Are you registering the bike under your name or selling it to someone else in your home country? Have you researched what the import tax is for your bike? I have friends from Singapore who had to stop their RTW motorcycle trip. They tried selling their bikes in Colombia where they were stopped in, but nobody would buy them because of how high the import tax was. They ended up abandoning the bikes in a parking lot with the keys in the ignition, because it was too costly to ship the bikes to the country of registration (bikes were bought in the US) to try to sell it there and then fly back to Singapore again.
We had the same issue in Kenya, tried to sell our SA-registered bikes there. Could not give them away because the import tax was greater than the value of the bikes. We had to ship the bikes back to SA, sell them bikes there and fly back to Canada. It worked out because we got another year of riding in SA, but if we didn't have to do that, it would have been (slightly) cheaper to abandon the bikes (or set fire to them) at the side of the road and just eat the cost of two motorcycles.
Import tax is no laughing matter. Most times, it's calculated at the time of first registration (so basically brand new) and in Europe can range anywhere between 25%-50% of the MSRP depending on the country. You don't want to face the prospect of having to either ship your motorcycle back to Canada or just abandon it in Europe because it's too expensive to register or sell it there.