Wells Fargo is the biggest mortgage servicer in the United States and you don't have a choice over who services your mortgage- mine was sold to Wells Fargo without my say. I could refinance but that comes with significant fees (>$1,000), I'd lose my amazing interest rate, and there is no guarantee it won't end up back in Wells Fargo's hands again.
[1]: https://www.nerdwallet.com/blog/mortgages/bbt-mortgage-revie...
Beyond that, this question is an imponderable for me because who can say what the future brings vs. the present. I guess one can refinance with some other credit union were this to happen in the future in a manner that was not desirable for one's mortgage.
The bank that held my parents mortgage was acquired no less than four times between 1996-2012. In 2007 I got a credit card from my local credit union - right now it's being transitioned into a Bank of America credit card. The credit union still exists though, they sold their credit card division to another company which then was acquired by BoA. Funny thing is a several years after they sold their credit cards they decided to offer them again and create new ones.
I'm asking because the hubby is I'm the military and he's the primary on our mortgage.