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Letting others know that you no longer want all the stuff they give you may be a bit tricky. But there must be a way to let your loved ones know that you no longer need all that stuff without making them feel like you don't appreciate the gifts they are giving you. I must confess that I never had the "minimalist talk" with any one in my family, but I do try to give them hints about my new lifestyle, and it's easier than you think.
For example, when people ask you what you want for your birthday, just tell them something that you truly need (if you do need something) or tell them to give you money, or something that is consumable, or maybe a well written card by them. Even if they think that what you ask is so little, just assure them that it is enough.
If you do want to have "the talk", just start by saying that you have been trying to change your life a bit, that you have been trying to surround yourself with people and moments, instead of object to remember those moments/people by.