I am starting an FNP program. Does this limit my options after graduation?

The school where I did my undergraduate studies offers three Master's programs for nurses. They are CRNA, CNS (Adult health), and FNP. My intent is to work in an acute care setting. I currently work in management, but my clinical background was in the ED, trauma unit, and ICU. I'm not positive where I want to end up, but I assume it'll be a similar practice area to what I'm used to. I'm thinking I want to work in an ED, ICU, or possibly some type of surgical specialty like plastics or ortho. I want a job where I assess, diagnose, prescribe, evaluate interventions, and adjust the plan of care accordingly. As a result, I think NP is the appropriate flavor of APN for me rather than CNS.

Will I be hindered by the fact that my program brands itself as an "FNP" program? I see that other institutions across the country offer programs they label adult NP, acute care NP, etc. My understanding is that they all lead to the same CRNP credential. As a nurse with experience and nursing certifications (CEN, CCRN, CNRN) will I be able to pursue the type of career I'm looking for after graduating from an FNP program? I'm enrolled in my first three classes at the moment, so I'm not too deeply invested.

Thanks!