For some services it is useful to have one name in the email header. When you create an email account, Google by default does not allow to leave the name field empty.
How to leave empty last name or both in Google Mail?
Hard way - or if you want empty both names
put to inputs special "Unicode Character" LEFT-TO-RIGHT MARK (U+200E) or ZERO WIDTH SPACE (U+200B) from "Char map" or online from section "Other Special Non-Printing Characters" https://coolsymbol.com