What Name do i choose for Domain Name Windows Server 2016 / Exchange 2016

I would have to fix the problem, that company.com not reachable from inside because of wrong resolution i would change DNS to send company.com outside and only have

company.com/owa and so on inside? is this possible?

No.  You'd need to maintain two DNS zones for that.  One DNS zone for the internal Active Directory network and one external DNS zone for web/email etc.

You should definitely use two different domains.  For example, company.com for the external domain (web/email) and ad.company.com for the internal Active Directory domain.
You really should host the Exchange server and Domain controller as separate servers.  Variant C is the better option.

Thank you very much for your opinion.
there is another question about domain name choosing:
years ago i had changed domain name due to server crash

old domain was
loooooongcompany.local

new domain
shrtcompany.local

i imported old mails via pst into mailbox, but on client side, i didnt know that import on server side is so easy now i think it was already Exchange 2010 but perhaps before that import export enabling service pack

the customer complained that the emails inside his outlook where not the same function as before

the old emails, if he clicked on the names where he sent the emails to it was treated like foreign domain..
i can not better explain i hope you understand what i mean.

anyway
The question is:
if i reinstalled this server now with Exchange 2016 and export the 2010 and import with 2016 via pst
can i
A)
change the
shrtcompany.local
to
ad.shrtcompany.com as we chose ariant 3?
or is there a problem with the treatment of the old mails again?

( i know there is a migration path from 10 to 16 but then i have the old sbs users and things from the old active directory.. i would like do do a fresh start, company is small not many users)

B)
if i stick to
shrtcompany.local
and import into the same way with pst then everything should be the same?

C)
if i do variant B) then for sure the server needs a local "Certifikation Authority" and we have to do local certs for inside traffic?

Best regards?

A)  I don't understand the problem with the emails.  The domain name of the server and the domain name used for emails are unrelated.  For example, the Exchange server could be called exchange1.company.local.  The email addresses are user@company.com.  The Exchange server is configured to use company.com as the email domain.  External URLs for the Exchange server are configured to autodiscover.company.com etc.  

B) again this depends on what the problems were before.  Without understanding the issues, I can't answer this.

C)  You don't need a CA.  You can purchase a certificate from a public CA.  This will work externally and internally.

Exchange will route email with x.400 addresses before looking at SMTP addresses. When the mailboxes were imported to a new domain they received new x.400 addresses, which is why you couldn't reply to old internal emails.