You can create an entry in Linode's DNS manager pointing to your home IP address. For example, if you are using example.org, you could create a "gameserver" entry which people would reach via gameserver.example.org. If for some reason this is impractical to do manually, you can use the
Linode DNS API to keep it updated. Note that the DNS zone files are generated at 0, 15, 30, and 45 minutes past each hour, so changes won't take effect instantly.
Edit: also, when changing DNS entries it may take some time for them to propagate; adjust your TTL accordingly. Just to be clear, Linode allows you to have DNS entries that point to a non-Linode IP address.