If you are only looking to replace all occurrences of "< " (with space) with "<" (no space), then you can do an lapply over the data frame, with a gsub for replacement:
> data <- data.frame(lapply(data, function(x) {
+ gsub("< ", "<", x)
+ }))
> data
name var1 var2
1 a <2 <3
2 a <2 <3
3 a <2 <3
4 b <2 <3
5 b <2 <3
6 b <2 <3
7 c <2 <3
8 c <2 <3
9 c <2 <3