Del. Code Ann. tit. 10, § 5904
(b) If a parent or legal guardian of a minor files a petition under this chapter and seeks to add that parent’s or legal guardian’s surname to the minor’s surname either as an additional name or hyphenated with the minor’s previously existing surname, or if a legal guardian who holds permanent guardianship of a minor files a petition under this chapter and seeks to change that minor’s entire name, there is a presumption in favor of granting the petition. A parent or legal guardian opposing a petition filed under this chapter has the burden to overcome the presumption by establishing by clear and convincing evidence that the totality of the following factors demonstrates that granting the petition would cause the minor more harm than benefit:
27 Del. Laws, c. 264, § 4; Code 1915, § 4660; Code 1935, § 5118; 10 Del. C. 1953, § 5904; 81 Del. Laws, c. 141, § 1; 81 Del. Laws, c. 332, § 1