Read a file line by line assigning the value to a variable

I encourage you to use the -r flag for read which stands for:

-r  Do not treat a backslash character in any special way. Consider each
    backslash to be part of the input line.

I am citing from man 1 read.

Another thing is to take a filename as an argument.

Here is updated code:

#!/usr/bin/bash
filename="$1"
while read -r line; do
    name="$line"
    echo "Name read from file - $name"
done < "$filename"

The following reads a file passed as an argument line by line:

while IFS= read -r line; do
    echo "Text read from file: $line"
done < my_filename.txt

This is the standard form for reading lines from a file in a loop. Explanation:

• IFS= (or IFS='') prevents leading/trailing whitespace from being trimmed.
• -r prevents backslash escapes from being interpreted.

Or you can put it in a bash file helper script, example contents:

#!/bin/bash
while IFS= read -r line; do
    echo "Text read from file: $line"
done < "$1"

If the above is saved to a script with filename readfile, it can be run as follows:

chmod +x readfile
./readfile filename.txt

If the file isn’t a standard POSIX text file (= not terminated by a newline character), the loop can be modified to handle trailing partial lines:

while IFS= read -r line || [[ -n "$line" ]]; do
    echo "Text read from file: $line"
done < "$1"

Here, || [[ -n $line ]] prevents the last line from being ignored if it doesn't end with a \n (since read returns a non-zero exit code when it encounters EOF).

If the commands inside the loop also read from standard input, the file descriptor used by read can be chanced to something else (avoid the standard file descriptors), e.g.:

while IFS= read -r -u3 line; do
    echo "Text read from file: $line"
done 3< "$1"

(Non-Bash shells might not know read -u3; use read <&3 instead.)