I have a restaurant named It dont matter family restaurant at the time i dint know there was another it dont matter restaurant about 60 miles away.

Conflicts over the name of a business can arise basically in two ways.  The most common conflict is encountered as a business first starts up.  Normally, the business is set up either as a corporation or as a limited liability company.  When someone forms either of these entities, it is necessary to reserve the chosen name of the entity through the office of the Secretary of State.  The Secretary of State, upon receiving a request for a name reservation, will search its records to see if there is another business entity somewhere in the State doing business under the same  or a similar name.  If so, the name will be disallowed and another name must be selected.  (Under prior law, the name of a limited liability company did not have to be reserved.  This enabled duplicated names from time to time.) The other area where such conflicts arise is where one business has trademarked the name and another business starts up using the same or a similar name.  The conflict ordinarily arises when the trademarked entity either sues the other or threatens to sue it.  Almost certainly the trademarked entity will prevail.  If that is your situation, you would probably do well to consider changing the name of your restaurant before you incur the cost and the bad publicity of a lawsuit.  If the other business is 60 miles away and the two of you are not in active competition with each other, the other business may be content to just leave matters alone.  If you have received threatening correspondence from the other business, you should consult a competent business/trial lawyer in your area.