So I am half Hispanic and half white. My mom was born and raised in Ecuador and my dad is American. I don’t look Hispanic and my last name definitely does not sound Hispanic, so should I still check the Hispanic box on college applications? My whole life I have been around Hispanic people, I know how to speak Spanish fluently, and I feel like its culture is my culture.
I just don’t know if there is a way to say that I am both, or if I should just say I am Hispanic.
Check the box you identify with. Or you can decline to state.
You can check as many of the boxes that apply as you want.
Hispanic or Latino people do not necessarily have Spanish sounding names. For example: https://en.wikipedia.org/wiki/Bill_Richardson
Your ethnicity is Hispanic and your race is white. Check the Hispanic box but be sure to show your culture in your application.
Given your background, there isn’t any reason not to check the hispanic box. Hispanics/latinos don’t look or sound a certain way. 
Yes. Check the box. Also, remember that there is a National Hispanic Recognition program (based on PSAT/NMSQT score) that you may qualify for.