From FarmersAlmanac.com:
Did you ever wonder, “Where do the month names come from?” Essentially, there are three sources: Greek and Roman deities, Roman rulers, and numbers.
May springs from the Greek goddess Maia, daughter of Atlas and mother of Hermes. She was a nurturer and an earth goddess, which certainly explains her connection with this springtime month, when flowers and crops burst forth.
June descends from Juno, wife of Jupiter, and the Roman ancient goddess of marriage and childbirth.
July was named in honor of Julius Caesar right after his assassination in 44 B.C., with July being the month of his birth. July is the first month in the calendar that bears the name of a real person, rather than a deity.