The issue with the water analogy is that it does not align with the Trinity doctrine, which teaches that God is one being in three persons, rather than a single person appearing in three different modes at various times.
As for your good question, Jesus anticipated what happened to the Corinthians, who broke up into factions and disunity.
1 Corinthians 1:10-17 Now I exhort you, brethren, by the name of our Lord Jesus Christ, that you all agree and that there be no divisions among you, but that you be made complete in the same mind and in the same judgment. For I have been informed concerning you, my brethren, by Ch-loe's people, that there are quarrels among you. Now I mean this, that each one of you is saying, “I am of Paul,” and “I of Apollos,” and “I of Cephas,” and “I of Christ.” Has Christ been divided? Paul was not crucified for you, was he? Or were you baptized in the name of Paul? I thank God that I baptized none of you except Crispus and Gaius, so that no one would say you were baptized in my name. Now I did baptize also the household of Stephanas; beyond that, I do not know whether I baptized any other. For Christ did not send me to baptize, but to preach the gospel, not in cleverness of speech, so that the cross of Christ would not be made void.
Evidently, Cephas and Apollos were making disciples and converts in Corinth. However, rather than recognizing that Jesus is the true teacher, several factions emerged, each favoring the person who baptized them. This confusion and disunity caused Paul to express relief that he had only baptized a few individuals. Jesus had clearly instructed the Apostles to baptize in the name of the Father, the Son, and the Holy Spirit, indicating that these three are the true teachers. It seems that Apollos and Cephas were unaware of this commandment.