Modern Greek has σκύλος for "dog," which is derived from ancient σκυλαξ, meaning "puppy." The generic word for a dog in ancient Greek was κυων. There is also a diminutive κυνάριον, which is of special interest because it occurs in a passage of the gospels of Mark and Matthew that is important in understanding the possible attitude of the historical Jesus towards the gentiles:
Mark 7:27 καὶ ἔλεγεν αὐτῇ Ἄφες πρῶτον χορτασθῆναι τὰ τέκνα· οὐ γάρ ἐστιν καλόν λαβεῖν τὸν ἄρτον τῶν τέκνων καὶ τοῖς κυναρίοις βαλεῖν.
28 ἡ δὲ ἀπεκρίθη καὶ λέγει αὐτῷ Ναί, Κύριε· καὶ τὰ κυνάρια ὑποκάτω τῆς τραπέζης ἐσθίουσιν ἀπὸ τῶν ψιχίων τῶν παιδίων.
24 From there he arose and went away into the borders of Tyre and Sidon. He entered into a house and didn't want anyone to know it, but he couldn't escape notice. 25 For a woman whose little daughter had an unclean spirit, having heard of him, came and fell down at his feet. 26 Now the woman was a Greek, a Syrophoenician by race. She begged him that he would cast the demon out of her daughter. 27 But Jesus said to her, "Let the children be filled first, for it is not appropriate to take the children's bread and throw it to the dogs." 28 But she answered him, "Yes, Lord. Yet even the dogs under the table eat the children's crumbs." 29 He said to her, "For this saying, go your way. The demon has gone out of your daughter." 30 She went away to her house, and found the child having been laid on the bed, with the demon gone out.
English translations such as the WEB seem to render this simply as "dogs," which clearly misses some further nuance, since Matthew uses the non-diminutive κυων in the sermon on the mount. My guess would be that Jesus simply means the kind of small dog that would be allowed inside a house where it could try to get human food. However, I've also seen it suggested that this is meant to mean a puppy, or that it somehow softens the harsh ethnic slur. (Matthew's version of Mark 7:27 makes it explicit that Jesus means this as a derogatory reference to gentiles.)
From contemporary English, we know that these animal labels for humans have connotations that depend completely on detailed knowledge of the cultural context. In current US English, if Jesus referred to a woman or her child as a "b----," it would mean something very specific. People without knowledge of our culture might misunderstand, e.g., they might say, "21st century Americans loved dogs and referred to them as man's best friends. Clearly calling a woman a b---- must have been a term of endearment." (Similarly, Jesus refers to Herod Antipas as a "fox," which isn't the same thing as what current USians mean by calling a woman a "fox.")
Is there any reliable information on what was meant in this time and place if a Koine speaker applied the term κυνάριον to an adult woman or her female child? And putting aside for the moment the question of applying the labels to humans, did σκύλος exist as the normal term for a puppy, or was it a koine word for an adult dog? And did koine κυνάριον in this period mean a small dog, a dog kept as a house pet, a puppy, or more than one of these?