You will need to file the I90 Application with sufficient proof of your legal name. There are specific instructions on the USCIS website and in the I90 Instructions on the process to correct the issued LPR card. This is more common issue then many people think and it is not difficult to remedy. Good luck.
Robin Jean GrayFamily Law AttorneyReading, PANJ licensed ·
You will need to file an I-90 form with the correct information and proof that the name as written in the I-90 form is correct. I would wait to travel until your name is corrected.