How to rename identical values in a column within R?

Say a data set:

a <- c(101,101,102,102,103,103)
b <- c("M","M","P","P","M","M")
dt <- as.data.frame(cbind(a,b))
dt

    a b
1 101 M
2 101 M
3 102 P
4 102 P
5 103 M
6 103 M

Column a is subject_ID, and column b is subject_name. I want to uniquely rename subject ID 101 to M1, and 103 to M2.

Is there a way to do this by indexing?

This does not work.

dt.try1 <- gsub("M","M1",dt[1:2,c(2)])
dt.try1
[1] "M1" "M1"

This is what would be ideal result:

    a  b
1 101  M
2 101  M
3 102  P
4 102  P
5 103 M2
6 103 M2

Why does not this work?