Domain is registered with one company and hosting with another. I am reading that to point the domain to the hosting I have to change the nameserver to point to the hosting company's nameservers. This would also mean I will have to move the MX records to the hosting company (the email is where the domain is registered). Can I create an A Name record that points to the IP of hosting without having to change the nameservers?
You don't need to point the NS records to your hosting providers name server. You can if you want to manage DNS together with your Web space, but it is also perfectly fine to manage your DNS externally. Just make sure, MX records point to your mail server and A/AAAA records to your web server's IP.
If you are using some sort of management interface on the side of your hosting provider (e.g. Plesk, cPanel etc.) you will still need to add any external domain there as well. Otherwise the domain would point to the server, but the server wouldn't have any vhosts for it and therefore wouldn't know how to handle it.
If you, however, don't want to use external DNS, then let the NS records point to your hosting provider's name servers. In that case any other DNS configuration will be done on those.