Wrong name on my green card

[MQ & MQ 6]

Hello everyone. 

I recieved my green card two days ago with all the information on the card being correct however the letter the approval letter that was sent a week before and the letter that came with the green card has something wrong with my name which is they used my first name my middle name my great grandfather name then my family name instead of my grandfather's name. Its a little bit complicated but on my passport my name goes like this: my name my father's name then the first letter of my grandfather's name which is the same letter for my great grandfather's name. On my birth certificate its all clear. Now i know it sounds really stupid but im afraid they messed my information and im a little bit anxious that this would cause a problem later when i apply to lift condition. After reading several posts it sounded like fixing a minor mistake would take 5 months plus. 

Does anyone know what to do?

Thank you