We hold God's name to be holy by interacting with others as Jesus did -- with respect, compassion, patience, and love.
Treating others rudely, disrespectfully, or indifferently denigrates both them and besmirches the name of their Creator. This includes the way we treat animals as well.
We hallow His name in prayer just as Jesus did in the disciples' prayer -- by beginning each prayer with salutations of respect and appropriate awe and by praying as Jesus taught us to pray.