What does Boaz mean?
Scholarly readings favor 'in him is strength' or 'in strength,' from be 'in' + oz (root '-z-z, 'to be strong'). An alternative traces it to a root meaning 'swiftness, quickness,' and Martin Noth preferred 'sharp mind.' The name of Ruth's husband and of a pillar of Solomon's Temple. The widespread name-site gloss 'swiftness' is weaker than the 'strength' reading; meaning is debated.
What does Ari mean?
From Hebrew ari (also aryeh), 'lion.' A short modern Hebrew name; distinct from the theophoric Ariel ('lion of God'). A concrete noun — its strength associations are connotation, not etymology.