in fact, I support LZ.
Whenever I signed contract with any vendors/customers, both my VP and lawyer
pariticularly pay attention that we spelled both names correctly, Inc and
Corp is not replaceable. Writing a research paper should be similar. In the
real world, you may get into trouble when referring others with the wrong
name.
It is a good thing that you pay attention to those details, that makes
difference in the real job.
When you start your actual work, in the similar case, however, you have to
be a little caustious when you pick up the battle.Some battle is worthy,
some, you should just let it go. That is the difference between persistent
and stubborn.
But in this case, if I were you, I will also bring it up. There are some
information just can't be messed up without telling people that you are not
professional, the company name is one of them.
I would stop here with only a thank you email.
I have learned in my past many years experience, if you think it is
important, then you should do your best to get your opinion pass. Be
persistent to the right thing is a differetiator between the leadership and
follower. Of course, how to judge what is important thing needs some
experience.