dat1 <- data.frame("name" = paste0("abc", seq(1:5)),
          "value" = round(rnorm(5), 1))


dat2 <- data.frame("name" = paste0("abd", seq(1:5)),
                   "other_info" = seq(11:15))

dat1$name2 <- sapply(dat1$name,
                        function(x){
                          char_min <- stringdist::stringdist(x, dat2$name)
                          dat2[which.min(char_min), "name"]
                        })
dat1