Feedback on my bash backup script
There is not a lot to say, the script is fairly simple.

For the date format:

file="${path}/$(date +%F).tar";


I think I would define a constant variable at the top of the code. You might want to change the pattern latter (use something different than YYYY-MM-DD).

This:

$(mkdir -p "$path");


can simply be written as:

mkdir -p "$path"


unless you want to save the output of the bash command to a variable but this is not the case here.



You have some key/pair values to define your backup sources:

dirs=(
    "/home/ferre/Minecraft"
    "/var/lib/automysqlbackup/daily"
);

# backup names
names=(
  "Minecraft"
  "Mysql"
);


I would combine both into an associative array.

declare -A sources=(
    ["Minecraft"]="/home/ferre/Minecraft"
    ["Mysql"]="/var/lib/automysqlbackup/daily"
)

for item in "${!sources[@]}"; do
  echo "Name: $item =&gt; Directory: ${sources[$item]}"
done


Output:


Name: Mysql => Directory: /var/lib/automysqlbackup/daily
Name: Minecraft => Directory: /home/ferre/Minecraft


Thus you can easily loop on the array and extract name and target directory. Warning: please check the syntax. Bash has many pitfalls and I may have made mistakes.



Logging: I think it is important to retain a trace of script execution. Especially when the script is unattended. The console can quickly fill up and you could miss critical messages.

You have a few options like:


define a variable for a log file then use tee -a next next to each command, so that you get output to console and to a file at the same time. But this is tedious and not flexible.
Call your script like this: /path/to/your/script.sh &gt; backup.log (use &gt;&gt; to append) or: /path/to/your/script.sh | tee backup.log
or better yet /path/to/your/script.sh 2&gt;&amp;1 | tee backup.log to capture the output of stderr.


Last but not least, your script could return an exit code. This is useful if your script is going to be handled by another script or even set up as a service.



Suggestions:


Have the script send you the log file by E-mail after execution. Or archive the log file somewhere for later review if desired.
Add error handling to make your script more reliable and more robust. If something wrong happens, or at least a fatal error, the script should stop and alert you. Here is an intro: Bash Error Handling


A backup script is usually critical, it has to perform reliably. One day, you may need to restore some important files, or recover from a system crash. There is nothing more tragic than useless/incomplete backups.

So you should also test your backups manually from time to time. Attempt to restore a random file and verify the result.