Name problem

Hello good day, 
I received my cheque and I was so delighted upon receiving it.
I am from foreign country and trying to deposit my cheque at a local bank. Although I’ve put my full name on turbotax and all the needed information and everything else on that check is correct they told me they’re not accepting my cheque because it’s not a complete name, the second name on my given name is missing on the cheque, Since it doest have my full-full name they cannot accept my cheque. 
I want to push through this and get my tax return money, but I have to make sure that IRS will accept my check. 
Is it possible that even though my second name missing I would still get my money?
 
I hope to get an answer soon, thank you for your understanding.