Baby names mean the same thing!

Elizabeth
So I already have a daughter named Virginia Mae meaning 'Pure' & 'Flower', we just found out we are having another little girl and plan on naming her after my Grandmother Lillian. But when I look up the name meaning it says "In English the meaning of the name Lillian is: derived from the flower name Lily. Symbol of innocence; purity; beauty." Basically Pure or innocent flower. Are the meaning too similar???