In Baptizing does one use "By" or use "In" in saying the name of Christ?

The correct "form" is: I baptize you in the name of the Father, the Son and the Holy Spirit (while pouring water over the head or immersing the person in water).

In the name of the father, the son and the holy spirit.  

We baptize IN the name of the Father, and of the Son, and of the Holy Spirit.

There are no requirements to say anything for a proper baptism to take place.  However, here's what Peter said on the issue.

Act 2:38  And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. 

And speaking of baptism, note that some falsely teach the following.

Whoever believes and it not baptized will be saved, but whoever does not believe will be condemned.  Later on if they want to, they can get baptized.

Baptism, which corresponds to this, does not now save you, ..., 

Here's what Jesus taught.

Mar 16:16  Whoever believes and is baptized will be saved, but whoever does not believe will be condemned. 

And here's what his apostle Peter taught.

1Pe 3:21  Baptism, which corresponds to this, now saves you, ...

Based on the above, here's how believers understandably and immediately responded to hearing the gospel message about Jesus (ref Ac 22:16; ref Mk 16:15).

Ac 8:36 ... “See, here is water! What prevents me from being baptized?” 

It rather depends upon the context of the situation you are speaking about.

John the Baptist said of Jesus -  "He will baptize you with the Holy Spirit and with fire" (Matthew 3:11 Mark 1:8).  In addition, "We were all baptized by one Spirit  -  (that's Holy Spirit)  -  into one body  - (that's being baptized into the body of Christ) - (1 Corinthians 12:13)  "For THROUGH Him  -  (that's through Jesus Christ), we both - that's both Jews and Gentiles - have access by one Spirit to the Father" (Ephesians 2:14)

We are also buried WITH HIM in baptism in which you were also raised etc....."  (Colossians 2: 11 - 13)

Most use "in" as in "I baptize you in the name..........."

The exact wording that the person uses isn't the main issue.  What matters is, is the person already saved?  You can't get water baptized unless you're already saved, and you can't add water baptism to getting saved.  See 1 Corinthians 1:17.  You can't add any works to getting saved.  See Romans 4:5.  If a person adds water baptism or any works to getting saved, then they are not saved at all. The Lord Jesus Christ is God, and He loves you.  Believing in the Lord Jesus Christ means being forgiven all sins past and future, and means going to heaven and not hell.  Death leads to immediate heaven or hell, and it is too late to be saved, after death.  All believers still sin.  See 1 John 1:8.  To be in heaven and not hell, believe in the Lord Jesus Christ, who is God and who died on the cross and shed His blood to pay for all of our sins in full, and who was buried, and who resurrected from the dead.  The only way to avoid hell is by believing in the Lord Jesus Christ, without adding any of your own works.  See Romans 4:5, 1 Corinthians 15:3-4, and John 3:16.

IN

Matthew 28:19 KJV — Go ye therefore, and teach all nations, baptizing them IN the name of the Father, and of the Son, and of the Holy Ghost:

Acts 2:38 KJV — Then Peter said unto them, Repent, and be baptized every one of you IN the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.

Acts 19:5 KJV — When they heard this, they were baptized IN the name of the Lord Jesus.

Acts 10:48 KJV — And he commanded them to be baptized IN the name of the Lord. Then prayed they him to tarry certain days.