My social security has four names because I'm on a H-1B so they took my whole name from the passport. At work I only use my first and last name on my documents so my W2 has first and last name only.

I basically use first, last name for everything banks, credit cards, etc..

Is that any problem that I ignored my 2 middle names?

Thanks.

Your name of the tax return that you file by you must match the SS records.
Even there is some difference of W-2, report the income and file the tax return.