You read the Scripture.
Did Jesus say anything to Peter to indicate at name change?
18 And Jesus walking by the sea of Galilee, saw two brethren, Simon who is called Peter, and Andrew his brother, casting a net into the sea (for they were fishers).
19 And he saith to them: Come ye after me, and I will make you to be fishers of men.
Mark 3:16
". . . Simon who is called Peter . . ." (DRA and DRB)
σιμωναG4613 N-ASM τονG3588 T-ASM (who) λεγομενονG3004 V-PPP-ASM πετρονG4074 N-ASM (TR with grammar superscripted)
The verb "lego" (= called, named, described as, referred to as) is in the present (continually ongoing) tense, passive (action by others than the subject) voice, and participle (-ing) mode; used as adjectivial singular masculine phrase may equally without argument say "is constantly being referred to as"
The time frame of the "is" includes and is from the vantage point of Levi/Matthew as he writes, Simon still also being alive, and of whom Levi is writing. Simon is still being called Peter, as of the writing. There is nothing here to suggest that "is" refers to the moment Jesus spoke to them, and most certainly not before that moment, or Levi could have used another tense to say "Simon was being referred to as Peter" at or before the time Jesus spoke to them, some time after His forty days of testing in the wilderness.
And don't call up Mark 1:12 to exclude Jesus' invoking the "Peter" concept just after (within 3 to 4 days) after His baptism but before His exit to the wilderness. The adverb translated "immediately" is used profusely by John Mark, 40 times, and can mean a few days or even a week (see verse 28). The timing is context-sensitive, but must agree with other inerrant, infallible Scriptures such as John 1:42, which happened about 2 or 3 days just after Jesus' baptism. Jesus did do the surnaming, as attested by other reference(s).