There's a few things to correct here.

First, although you ask for user-input via read, you don't actually use the result anywhere. By default, read assigns what's read to a variable named REPLY so you'd want pidof -x "$REPLY"

Second, inside [ ... ] POSIX test brackets, > has its ordinary meaning as a redirection operator¹. If you check your current directory, you will likely see it now contains a file named 0. The integer "greater than" test is -gt.

Third, your pidof -x inside the [ ... ] test is just a string; to execute it as a command and capture the result you need command substitution

[ "$(pidof -x "$REPLY")" -gt 0 ]

However, pidof may return multiple integers if multiple matching processes are found - which will cause yet another error. So I'd recommend instead using the exit status of pidof directly:

EXIT STATUS

       0      At least one program was found with the requested name.



       1      No program was found with the requested name.

So you could do

#!/bin/bash

while true

do

read -p "Enter the name of process: "

 if pidof -qx "$REPLY"; then

    echo "exists"

 else

    echo "does not exist"

 fi

done

¹ inside a bash [[ ... ]] extended test, > is a comparison operator - however it performs lexicographical rather than numerical comparison, so you'd still want -gt there. You could use > for integer comparison inside an arithmetic construct (( ... )) though.