Europe's Turtle Doves were commonly known as "turtur" which imitates the birds' call. Around 1500, the final "R" was replaced by an "L", making the often-translated biblical phrase "...the voice of the turtle is heard in our land" make a tiny bit of sense.
The Mourning Dove is a very common bird - with over 400-million of them in North America. Which is a good thing, odds wise; about 70% of young doves die in the first year. But they adapt well to a human-directed environment, unlike its Passenger Pigeon cousin which was once touted as the most abundant bird in the world (but is now extinct).
You can attract Mourning Doves to your yard, but keep in mind that you might attract other kinds of doves too. They tolerate birdfeeders, but prefer to pick through seed scattered on the ground. (Better footing!) Doves have a tough time with ordinary tube feeders, where the relativelty short perches don't accomodate relatively large birds. Also, make sure you have several large shrubs around, so they can nest undisturbed. In warm weather birdbaths are also a big draw.