Three person Euchre is definitely a real thing and there are ten different ways to play it, according to Wikipedia. They pretty much all rely on:
- Setting extra cards aside as a dummy hand (more rarely, removing cards from the deck or adding cards to the kitty)
- Having players keep track of points individually, since they don't have a consistent partner (if they have a partner at all)
The one you described, Canadian Euchre, is indeed one of those ways, (it is also called Buck Euchre, especially in the Midwest of the United States, where I have indeed seen it played).
Four hands are dealt out, one to each player and one face down on the table. The dealer turns up the top kitty card, as usual, and this card is automatically trump; there is no bidding for trump. Instead, each player has the option, in clockwise order starting at the dealer's left, of playing the dealt hand or the blind hand on the table. If the player picks up the blind hand, he places his hand face down on the table and that becomes the new blind hand. Interesting play results if two (or more) players pick up the blind hand because the original owner of the hand knows what they have.
When bidding gets to the dealer, the dealer picks up the trump card and play begins. Normal Euchre play now applies, with each player on their own. At the end of the hand, each player gets one point for each trick taken. If a player takes no tricks, he loses five points.
Another one that I find is pretty common (at least in my region) is "Three Hand Dummy" Euchre, in which you set aside cards as if you had a fourth player, but just ignore them:
Another common three-player variation is played by dealing out four hands, but with the fourth hand acting as a dummy hand, known in different places as "the dummy," "the dead hand," "the imaginary friend," or "Johann." The player who calls trump on the current hand picks up the dummy hand and makes the best five-card hand for themselves out of his or her hand and the dummy hand. The player will now play alone against the other two players, who will play as partners for this hand. The two non-calling players will always play as partners which means that partners will switch from hand to hand depending on who calls trump.
The calling player will score one point for winning the hand and 2 points for taking all five tricks. The calling player can still elect to "go alone" by choosing not to pick up the dummy hand. Taking all five tricks here results in four points. Each player keeps their own score.