Name spelled wrong

Ugh just got my daughters SS card in the mail and her name is spelled wrong! Which means her birth certificate will be wrong as well. I can understand the misspelling as her name is Elsie and they put Elise. But that means I have to correct it on her birth certificate, request her corrected birth certificate then take it all the way to the SS office to get a new card with her corrected name! Has this happened to anyone else?! This is the last thing I want to have to take on as a new mom. 🙄