I got married in 2024 and my name is different on my W2 than my Social Security Card, will this cause issues when filing my taxes?

I was able to change my name on my social and my drivers license, but my employer is still dragging their feet to update for employment records. So, now my W2 will still have my maiden name. Do I have to wait for a corrected W2 or can I file as is? Which name do I use? Also, I added his last name to mine without hyphenating, if that makes a difference.