Why players make alts
Almost always for profit. Every new account gets a starter kit, a daily reward, a bonus for inviting a friend or one more vote on a server list. Ten accounts bring in ten times as much, the resources flow to the main account, and the server economy gets out of balance.
Less often an alt is used to store items, to get around a clan limit or to enter a contest several times.
If someone came back on a new account after a ban, that is ban evasion. It has its own guide: how to deal with ban evasion.
Rules and rewards first
Decide what is allowed on your server. For example, a second account is fine, but farming rewards on alts is not. Put this in the rules, and you can ban for breaking it without arguments.
The reward system itself helps too. If a reward depends on time played rather than on simply logging in, alts stop paying off.
Close VPNs and proxies
From one home connection all the alts join from one address and are easy to spot. That is why farmers hide their accounts behind VPNs and proxies. Once such connections are closed, all of a person's accounts are left with their real addresses. To set this up, see how to block VPNs and proxies.
How to find alts
On any plan, a player's profile in the Kordon panel has "Related players": nicknames that joined from the same addresses. If one of them is already blacklisted, the panel marks it.
On Premium and higher the same place also has the account links graph. It finds one person's accounts by more than shared addresses and shows the strength of each link: "Probably one person", "Possible link" or "Weak link". A time slider shows the links as of the date you pick. The graph looks only at your server, so you will not see accounts on other servers.
If the link is strong and the violation is obvious, you can blacklist the whole group with one button, "Block the whole group".
Do not rush to ban
One shared address proves nothing: behind it may be a family, a dorm or a mobile carrier with hundreds of subscribers on one address. Before banning, look at when the accounts joined, what they played and where the resources went. If in doubt, message the player. An honest person will usually explain who else plays on their computer.