If it's a thornless plant and it has flowers on the primocanes (stalks that came up from the dirt this growing season), it's probably a Joan J raspberry.

If it's a Joan J, you'll get fruit this fall on this year's growth, and then in the spring again on the same canes. It'll repeat the process next year by sending up new primocanes that will fruit next year in the fall and then the following spring after that.

Thank you for the name. I have no idea what a primocane looks like and I'll have to watch it carefully to see if I can spot one. However, looking up the name on google, I read that Joan J is not the best raspberry and is best known for its shipping attributes. I'll give it until next year to see if it is worth keeping. There must be a reason the other person didn't want the plant. I had planned to put it in a barrel in 2014, but I might just hold off on that. It is sad, because it is growing extremely well and looks very pretty.