Adding the LETTER ‘e’ adds no cute effect.
‘Ann’ and ‘Anne’ are variant spellings of the same name. They are pronounced the same way. Sometimes the extra e is there because it represents a deliberate archaism, as in ‘shoppe’, or a spelling borrowed from French or another language (especially girls’ names: Anne, Jeanne, Claudette, Noelle, etc.), as was said above.
‘child’ and ‘childe’, however, are different words. ‘Childe’ is an obsolete word that refers to a child of noble birth, perhaps somewhat like ‘infante/a’ in Spanish, but referring to any noble child, not just the child of a king.
Adding the “long e” SOUND as an extra SYLLABLE (usually spelled -ie, -y, or -ey, with the preceding consonant doubled if necessary to keep the vowel in the previous syllable short; less commonly -i or -ee) at the end of the word is the English diminutive, like ’-ito/-ita’ in Spanish, e.g., ‘John/Johnny’ = ‘Juan/Juanito’.
Centuries ago, those silent ‘e’s were pronounced, by the way.