W-2 and 1099 int

2 things, So I forgot to inform my old employer of name change after marriage, I called them to correct my w-2 and 1095. They said they will update my account and that I can edit my copies to reflect my new name but that they will not send me a w-2c. Will that cause any issues when I file? (I already updated ssa a while back so I have my card with my new last name).

Also I forgot to update my name at my high yield savings account so I received a 1099-int with my old name but I called them and informed so they should be updating it but anyways they said they will not issue me a new 1099-int because it reflects what the name is on my account so what should I do because I’m stressed