I think the quotes were to point out the previous commenter’s use of Dr. Smethurst’s first name in that way could be considered diminutive. Unless Dr. Smethurst prefers to be known as Dr. Becky or the commenter has a personal relationship justifying the familiarity, it may be impolite to use “Dr. Becky.” If she does use that form, antiquemule may have been unaware of it or may consider it impolite nonetheless.