How important are the names on our train tickets?

I have not had anyone check IDs ever on trains in Europe including trips we took a couple of weeks ago on the TGV in Brittany and last spring when we took it to Reims. IN fact on the trips recently no one even checked tickets at all; last spring they checked but not ID. We have traveled on trains occasionally over the last 50 years. But of course yours might be the one time. I personally would't give it a thought and I am usually pretty conservative about risk.

Thanks, Janet, for your quick reply! Although we've done a fair amount of train travel in Europe, it's never been in France, so I wanted to make sure. Thanks again!

If the names are simply reversed, I wouldn't think twice about it.

Amy,

It's highly unlikely that they would look at names unless you're using some kind of personalized discount pass (such as a weekend pass or a senior pass), which might cause them to check to make sure the person entitled to the discount is the one attempting to use the pass. I've never had that done to me personally.

Even if they would check, I can't imagine it being a problem because it is common in France to switch the first and last name. For example, my debit card from BNP Paribas lists my name as "M. LASTNAME FIRSTNAME. I've seen reversed names routinely in the signature block on business correspondence. You may even see small businesses (painters, remodelers, plumbers, etc.) as you walk around with signs on their work vans where the two are switched, if the proprietor wants to emphasize his or her last name (often, the last name is all caps whereas the first name is initial letter capitalized only).

No big deal-
If it is a print-at-home ticket they should check your ID (passport) to stop you printing out a second copy and giving it to someone else to use. But frequently they don't bother. Conventional tickets (from a ticket machine or a manned counter) do not have names on them.
A back-to-front name should not be an issue, it is obvious who was meant.

"Since it's not an international train journey," - that won't make any difference, either way.

Thanks, everyone!