The new covenant did not start while Jesus was on earth, it started when Jesus finally fulfil the law. His name while on earth was not yet officiated as the new high priest as evident in the verse below;
For if He were on earth, He would not be a priest, since there are priests who offer the gifts according to the law; Hebrews 8:4 NKJV
Hence, He said in Mat 28:19 go and baptised in the name of the father, son and holy spirit. After He fulfil the law where the name became official, apostles then baptised in the name of Jesus Christ because, they understood that the name of the father, son and holy spirit was after all Jesus Christ.
Ironically, those who believe as according to the above also believe in tithing because of Matthew 23:23 to which Jesus said we also ought to tithe, the same Jesus who did not yet acknowledge His own name to be the name of God, Son and holy spirit because, while on earth He cannot be high priest since there were priest who offer gifts according to the law. Don’t you think since He does not acknowledge Himself as the high priest yet, its natural for him to still acknowldge that the tithing which was given by God as inheritance to the levites still ought to be given to them becuase they were still needed to function. After the fulfillment, we don’t need the service of the levitical priest to offer gifts and sacrifices, we can now directly offer sacrifices and communicate to God through Jesus Christ. Yet, some believe we still need to pay 10% as if Jesus did not yet fulfil the mission yet.