Is it ok to file h1b with incorrect i94 name details

I had to urgently travel to India on March first week and I cam back on March 14 but one of my first names is missing in the i94 after poe. I tried with a cbp officer at chicago to change the wrong i94 name but he doesn’t have a clue on this to change .so I need to file h1 on April 1 and I am not sure on how long it takes to.change this wrong i94 name . Is it ok to file with a wrong i94 name for H1 ?