Is it inappropriate to change my last name to a Jewish one?

Good evening everyone!

Let me preface this question to say that I was adopted by a non-Jewish couple and raised in a secular household and was given their last name. I’ve been told that my father was a Hispanic Jew and my mother was white. That’s all I know about their backgrounds,
Like I said, I was raised secular but found myself drifting into Judaism into adulthood, have since converted, and have been a practicing Jew for about 5 years now. Lately, I’ve been considered changing my surname from my adoptive parents’ name to a Jewish or Sephardic name. As much as I love my parents, I really want to feel connected to my heritage, my culture, and my religion. The thing about it is that I have no biological family names to go off of and would have to select my own. My question is, would it be weird or inappropriate to pick a random Sephardic or Jewish last name if I don’t come from those families?