Thanks for the responses! I know a lot of people do it, am just a little scared. Plus when I talked to someone at IRS he told me that I need to change SSN with my employer first because if I file a tax return where my SSN does not match the SSN on the W2, the employer and I will be contacted to prove that the number actually belongs to me! This is not something that I want to go through especially while my GC is pending.
Otherwise, a lot of taxes were taken out and am owed a refund; I just want to do it in a way that won't affect me down the road