Here’s what Luke writes in regards to the lineage and situation of the Baptist’s parents and the annunciation of his upcoming birth:

“In the days of Herod, king of Judea, there was a priest named Zechariah, of the division of Abijah, and he had a wife from the daughters of Aaron, and her name was Elizabeth. And they were both righteous in the sight of God, walking blamelessly in all the commandments and righteous requirements of the Lord. But they had no child, because Elizabeth was barren, and they were both advanced in years.” Luke 1:5-7

And:

“And an angel of the Lord appeared to him, standing to the right of the altar of incense. And Zechariah was troubled when he saw the angel, and fear fell upon him. But the angel said to him, ‘Do not be afraid, Zechariah, for your prayer has been heard, and your wife Elizabeth will bear you a son, and you will call his name John. And you will have joy and gladness, and many will rejoice at his birth. For he will be great in the sight of the Lord; and he will not drink any wine or strong drink, and he will be filled with the Holy Spirit while yet in his mother’s womb. And he will turn many of the sons of Israel back to the Lord their God. And he will go before Him in the spirit and power of Elijah, to turn the hearts of the fathers back to the children, and the disobedient to the attitude of the righteous, to make ready a people prepared for the Lord.’” Luke 1:11-17

The name Zechariah in Hebrew means “remembered by Yah,” or Yahweh remembered:

Zekaryah

Strong’s Exhaustive Concordance

Zachariah, Zechariah

Or Zkaryahuw {zek-ar-yaw’-hoo}; from zakar and Yahh; Jah has remembered; Zecarjah, the name of twenty-nine Israelites — Zachariah, Zechariah.

see HEBREW zakar

Strong’s Concordance

zakar: remember

Original Word: זָכַר

Part of Speech: Verb

Transliteration: zakar

Phonetic Spelling: (zaw-kar’)

Definition: remember

see HEBREW Yahh

Strong’s Concordance

Yah: the name of the God of Israel

Original Word: יָהּ

Part of Speech: Proper Name

Transliteration: Yah

Phonetic Spelling: (yaw)

Definition: the name of the God of Israel

Elizabeth’s Hebrew name means “(my) God of an/the oath”:

Elisheba

Strong’s Concordance

Elisheba: “God is an oath,” the wife of Aaron

Original Word: אֱלִישֶׁבַע

Part of Speech: Proper Name Feminine

Transliteration: Elisheba

Phonetic Spelling: (el-ee-sheh’-bah)

Definition: “God is an oath”, the wife of Aaron

NAS Exhaustive Concordance

Word Origin

from el and shaba

Definition

“God is an oath,” the wife of Aaron

NASB Translation

Elisheba (1).

Brown-Driver-Briggs

אֱלִישֶׁ֫בַע proper name, feminine (God is an oath, by which one swears, compare Isaiah 19:18; Amos 8:14; Zephaniah 1:5) wife of Aaron Exodus 6:23; = Ἐλεισαβεθ ᵐ5, compare Luke 1:7.

And here’s the meaning of John’s Hebrew name:

Yochanan

Strong’s Exhaustive Concordance

Johanan

A form of Yhowchanan; Jochanan, the name of nine Israelites — Johanan.

see HEBREW Yhowchanan

Strong’s Concordance

Yehochanan: “the LORD has been gracious,” the name of a number of Isr., also a son of Tobiah

Original Word: יְהוֹחָנָן

Part of Speech: Proper Name Masculine

Transliteration: Yehochanan

Phonetic Spelling: (yeh-ho-khaw-nawn’)

Definition: “the LORD has been gracious”, the name of a number of Isr., a lso a son of Tobiah

NAS Exhaustive Concordance

Word Origin

from Yhvh and chanan

Definition

“the LORD has been gracious,” the name of a number of Isr., also a son of Tobiah

This is how one lexicon defines Hebrew term chanan:

chanan

Strong’s Concordance

chanan: beseech

Original Word: חָנַן

Part of Speech: Verb

Transliteration: chanan

Phonetic Spelling: (khaw-nan’)

Definition: to show favor, be gracious

Brown-Driver-Briggs

I. חָנַן verb shew favour, be gracious (Late Hebrew id., Aramaic חֲנַן ; Arabic  yearn towards, long for, be merciful, compassionate, favourable, inclined towards; Sabean חן in proper name חן מסבררהם DHMEpigr. Denkm. 40; Phoenician חנן in חן favour, and proper name as אלחנן, חננבעל; Assyrian in derivatives annu, grace, favour, unninu, têninu nannu, id., LotzTP ZimBP 23, 66) —

Note again the meaning of these names: Zechariah (“Yah remembers”), Elizabeth (“God of an oath”), John (“Yahweh has been merciful/compassionate/gracious”).

With the foregoing in perspective notice what the Holy Spirit inspired Zechariah to say after his son John was born:

“And his father Zechariah was filled with the Holy Spirit, and prophesied, saying: ‘Blessed be the Lord God of Israel, For He visited and accomplished redemption for His people, And raised up a horn of salvation for us In the house of David His servant—As He spoke by the mouth of His holy prophets from of old—Salvation from our enemies, And from the hand of all who hate us, To show mercy (heleos) toward our fathers, And to remember His holy covenant, The oath which He swore to Abraham our father, To grant us that we, being rescued from the hand of our enemies, Might serve Him without fear, In holiness and righteousness before Him all our days. And you, child, will be called the prophet of the Most High, For you will go on before the Lord to make ready His ways, To give to His people the knowledge of salvation By the forgiveness of their sins, Because of the tender mercy of our God, With which the Sunrise from on high will visit us, To shine upon those who sit in darkness and the shadow of death, To direct our feet into the way of peace.’” Luke 1:67-79

The Greek term for mercy also means compassion:

Strong’s Greek 1656

eleos: mercy, pity, compassion

Original Word: ἔλεος, ους, τό

Part of Speech: Noun, Masculine; Noun, Neuter

Transliteration: eleos

Phonetic Spelling: (el’-eh-os)

Definition: mercy, pity, compassion

Usage: pity, mercy, compassion.

Here’s where we see the Spirit at work:

“To show mercy (Jochanan) toward our fathers, And to remember (Zekaryah) His holy covenant, The oath (Elisheba) which He swore to Abraham our father,” Luke 1:72-73

It is apparent that the Spirit moved Zechariah to employ the phrases “mercy,” “remember,” and “oath,” in order to make the connection with the names of John and his parents. The Baptist and his parents were all signs of God’s having remembered the oath he had made to the fathers which he was now graciously fulfilling though the miraculous birth of John, whom God appointed to be the forerunner to the Messiah Jesus!

FURTHER READING

The Revelation of the Gospel in Adam’s Genealogy