Yes, this is possible!
The easiest solution is using an SRV record. SRV records are spiced-up CNAME records. They return not only the domain with the correct A (or AAAA) record but also the port.
So assuming you have the domain meinedomain.de with an A record pointing to the IP 1.2.3.4 where the TeamSpeak server can be reached on port 9999.
You can then simply add the SRV record _ts3._udp.meinedomain.de with the target domain set to meinedomain.de and the target port set to 9999. This will allow users to connect using meinedomain.de and the port specified.
For ts.meinedomain.de you can do the same but name the SRV record _ts3._udp.ts.meinedomain.de. The target domain can either be meinedomain.de or ts.meinedomain.de.
There are also a lot of tutorials specifically for TeamSpeak SRV records, specifically for your domain’s DNS provider.
Also, check this out:
Alternatively not exactly what you are asking for, but you can also use the TeamSpeak server nickname feature. To quote myself:
