I was looking for a one syllable girl's name that was only 4 letters long. All ideas are welcomed, also I would like to know what letter could be added to any name that wouldn't change how it was pronounced.

One syllable girl names with 4 letters include:

Anne, Bess, Beth, Cass,
Dawn, Elle, Fern, Flor,
Gail, Gwen, Gwyn, Hope,
Jade, Jane, Jill, Joan,
June, Kate, Lynn, Maud,
Rose, Ruth, Sage, Tess

As to your second question... I don't know of a letter that can be added to *any* name in that way, but specific letters in specific cases do work like that -- for instance, you can often double the last letter, if it's a consonant (Scarlet/Scarlett, Lyn/Lynn) or add an "e" (Clair/Claire, Sloan/Sloane).