It is forbidden to destroy holy Names and writings, as this is a disgrace to G-d's honor and profanes His Name. Minhat Hinuh Commandment 69 (in his Kometz Minha) writes that one who erases G-d's Name has done no less of a transgression than one who mentions His Name in vain, and both are thus clearly forbidden for Gentiles.
The Hebrew Names which may not be destroyed are: Y-H-V-H, Ado-nai, Ai-l, E-lohim, E-lohah, Sha-dai, Tziva-ot, Ehe-yeh, and Y-ah, and any of the possessive versions of E-lohim, such as Elo-hehah, or E-lohaihem, or E-lohainu and the like; even to erase one letter from one of these Names is forbidden.
However, if one only wrote part of a Name, such as "Shad" from Sha-dai, or "Eh" from Eh-yeh, or "Ado" from Ado-nai, since he does not complete the Names, he may erase them if there is a need to do so. However, it is forbidden to disgrace them (the Divine Code by Rabbi Moshe Weiner, Ask Noah International, 2011, p 273-274).