This could be a number of things.
First of all, go to your character and make sure you have the mesh set to use the correct animation blueprint.
It could also be the Blend Space. Make sure you have idle on all the spots that could possibly be 0 speed.
It could also be the animation graph not setting the speed correctly. Try putting a print string to your speed variable and make sure that the graph thinks you are at 0 when your character isn’t moving.
Finally, make sure the rules for your state machine that gets into and out of your idle/run are correct. Also, is there any other animation state that you are using in your state machines that looks like a run that might be getting triggered?
Those are the main ones I would think would be causing the issue.