In normal usage, I think the word is "traditionalist".
"Paleophile" would be a better word but I don't find it in any dictionary: it's not an accepted word.
- Very late addition and clarification *
If there is no well-known word that expresses an idea you want, you can, of course, always make up a word or use a word that somebody else made up and that only 10 people in the world know. But then you can't expect your readers to know what it means. You'd have to define it. Don't make up a word or use an obscure word with no explanation.
If you would only use this word once or twice, I'd say, in general, don't. Just use a phrase to explain what you mean. If you need to use the word many times so that using the same phrase over and over would be awkward, then sure, invent a new word, define it, and then use it.
Like, "These people are what I will call 'paleophiles', by which I mean, people who love old or ancient things. Paleophiles often ..." etc.
The person providing the service is an agent.
agent noun
1 a person who acts on behalf of another, in particular:
• a person who manages business, financial, or contractual matters for an actor, performer, writer, etc.
• a person or company that provides a particular service, typically one that involves organizing transactions between two other parties.
[ODO]
I would suggest client for those whose transactions he is managing.
Best Answer
A cashier would be one option. In more up-market establishments it may well be the maître d'hôtel (often abbreviated to maître d') who would handle these payments, though not necessarily while sitting at a counter.