Quoting Commentary for II Kings 4:16

ותקרא את שמו שלה והיה בכזיב בלדתה אותו, “she called his name Shelah, as he (her husband) was in a place called Keziv at the time when she gave birth to him.” (standard explanation) The expression “shelah” and “keziv,” are identical in meaning. They appear in connection with inability to give birth, such as in Kings II 4,16 when the woman from Shunem being promised by the prophet Elisha that she would give birth to a son tells him not raise false hopes as she knew she was past the age when this was possible. The words she used were אל תכזב. When she upbraided the prophet after the son she did bear had died before growing up, she reminded him of what she had said then and used the verb שלה. (verse 28 in the same chapter) The word כזב meaning interruption in the sense of termination, also occurs in Isaiah 58,11: וכמוצא מים אשר לא יכזבו, “like a spring whose waters do not fail.” According to this, the name shelah indicated that his mother knew she would not bear any more children. [This leaves the question of why the masculine והיה, “he was,” is used in our verse Ed.] My teacher told me that כזיב is the place of a town or village. It was customary in those days that mother and father named their children alternately. The father would name the firstborn, so that it would have been Yehudah’s turn to name the son born third. Seeing that he was not at home when this son was born, the mother decided to name him instead. This is why the Torah explains why Yehudah had not named Shelah.

3. The announcement is formulated as "at this season, next year … a son." (Melachim II 4:16 / BeReishit 18:10).

שוב אשוב I WILL CERTAINLY RETURN — The angel was not announcing that he would return to him, but he was speaking to him as God’s agent (meaning that God would return). Similar is, (16:10) “And the angel of the Lord said to her, I will greatly multiply thy seed, but he had no power to multiply, and was speaking only as God’s agent. So also here, he spoke thus as God’s agent. Elisha said to the Shunamite (2 Kings 4:16), “At this season when the time cometh round thou shalt embrace a son”, and she said, “Nay, my lord, thou man of God, do not lie unto thy handmaid; see, those angels who made the announcement to Sarah said “at the appointed time I will return”! Elisha in effect said to her, “Those angels who live and endure for ever could indeed promise “at the appointed time I will return”, but I am only flesh and blood (human), alive today and dead tomorrow — but whether I live or die, “at this season [thou shalt embrace a son]” (Genesis Rabbah 53:2).