To change your summoner name to a name that is already taken, the account with the name you want needs to be inactive for a certain # of months.
For accounts that are level 6 and below, you need to wait a minimum of 6 months before you are able to take the name for yourself.
For each level above 6, add one more month to the wait, so level 12 would be a year, level 24 would be 2 years, all the way up to level 30 being 2 1/2 years.
So, for your particular situation, since the summoner name you want is only level 3, you will need to wait until that account has been inactive for 6 months total. After that, you are free to take the name. Also, you can always go to the account name change in the store and type in your desired name to check if it's available.