What to communicate to family and friends when parent enters hospice?

You are free to share what your elder will allow you to share. I am uncertain what you mean about what to communicate. Most people are well aware of what hospice is. If they are not they can google hospice care. Or you can let them know that your mother's condition now is incurable, and that she has made the decision to decline further care aimed at "cure" and to accept that he life will likely end now, within a certain unknown time frame. Let them know she will receive extra services now, hospital bed if needed, special nurses, aids to assist with activities of daily living, clergy if she wishes, social workers. Tell them she will not be taking medications that are meant to "cure" where there is no cure, but will be kept pain free and free of air hunger. Basically it is "June, Mom isn't going to get better. Her disease has progressed to the point where there cannot be a cure, and where any meds and tests aimed at cure will likely cause her more pain and grief that not. She is going now into "comfort care" so that she can concentrate on being with her family, being kept comfortable." That is sufficient. Encourage people not to say things like "Oh, you CAN get better. Have some Turmeric tea. That cured Aunt Betsy when we all thought she was dying". These things don't help. Let your Mom lead any conversation. Don't deny her words. Tell her you are sorry, that you care for her and ask what you can do to help her now.

Tell friends and family that you want to keep informed that “Ruth or John” is now on Hospice.
You can ask your Hospice if they have a program (actually an app) called TapCloud, there may be others. But family can easily be kept up to date on the condition if you wish that.
There is another site called CaringBridge that you can use to keep friends and family up to date.

In all situations in my family (aunts, uncles, my mom) we called or emailed and said " X is now in hospice care". It indicated to everyone that the end of life was very near.

If we had signed on to hospice care when mom was first eligible, I would have said "mom is now under hospice care but she is not in immenently dying. She has chosen comfort care over repeated trips to the ER which are distressing and which are not improving her health".

You just tell them the truth. I'm guessing it's your father that you have listed under your profile who has cancer, so you tell them that your father has decided against any further treatments for his cancer, and that he has opted for hospice care to keep him comfortable until he passes.
If he is at home with you, then you can control who comes to see him and when, and like Isthisrealyreal said, if they ask how they can help, tell them. As you are discovering, hospice does but only a very small potion of your fathers care, so don't hesitate to ask family and friends to help you in any way they can.
Please try and make the best of whatever time you have left with your father, and don't leave anything left unsaid. God bless you and your father.

You just tell them that she has decided that quality is more important than quantity and she is on hospice. Then tell them when they can come visit and what they can do to help, if they ask.