It's a good idea to tell someone where you are going and how long you will be. But don't worry about ppl looking at you. Normally ppl don't care about runners and no one who sees you will have any idea how long you have already been running for (not that they care anyway) just go out and enjoy it.
I have an ID wrist band with my name and the name and phone number of my partner on it, and allergy advice so in case something happens to me ppl will know who I am and who to contact.
Good luck with your running!