Both my dcs have family names incorporated in their names. It's not done in the traditional John and John Junior etc way but they are there.
For us it was one of many ways of connecting our dcs to the family they came from and of showing our love for the people in our family who those names were relevant to.
We were under no pressure or expectation to do this though and wouldn't have done it if we didn't like the names we incorporated into their names.
That said, both times the person in question cried when they realised the connections we were making and were very touched by the genuine affection it showed.
I would also say that, possibly coincidentally, both my dcs have particularly close relationships to those people they are named in honour of.
We have a tiny family on my side and because of the way things have gone our family surname is going to die out with my dbrother and myself. 
At least this way my dcs still carry on some link to their heritage.
I do have to say that, if it was being even gently forced upon me, I would have rebelled and gone in completely the opposite direction - especially if the pressure had come from dh's side as the dcs already carry their surname.
I don't think you should be made to call your own child anything but what you want to call them and that you have the right to choose and love their name. I am simply explaining why we chose family names.