Is this a raspberry bush?
Yes, It looks like a summer bearing red raspberry.
They put up new shoots from the ground every year. These shoots bloom fruit and die the second year. Remove old shoots at the end of fruit harvest but keep the new shoots. In early spring (end of March) thin out the one-year old canes to one every 8 inches. Keep the big ones and remove all others. Cut back to about 30 inches tall.
I suggest you pick fruit every other day. Raspberries are very attractive to SWD (spotted wing drosophila) which will quickly ruin the fruit.