Last name troubles

I've been thinking about this for a long time but it's been a year since my dad passed and I've decided I am going to try to add my mothers maiden name onto mine. A hyphenated situation... we are getting started with this process and it might take a while... to anybody whose gone through that before, any advice? And I will be receiving my letterman soon, what last name should I put? And would it be offensive to put my mothers?

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