Bank tellers get their name from an Old English word that means "to count."
History of The Word
The modern words "tell" and "teller" are both based on an Old English word, "tellan," which in turn is based on a similar Germanic cognate. The original definition of tellan was "to reckon, calculate, count, consider or account." Over time the word has evolved into "tell,"
The word teller dates back to around the end of the Fifteenth Century, with the traditional definition "person who counts." It eventually came to refer to a bank teller.
Evolution of Meaning
The words tell and tellan in its earliest days had two separate meanings. The first was as mentioned above, "to count, reckon, etc." The second was "to inform, narrate." Over time, the first meaning of the word fell out of use. In modern times, we know the word tell only by its latter meaning.
The Word is Like a Fossil
Apparently, the word "teller" was coined to describe a bank clerk before the word "tell" shed its first meaning, "to count." Today we refer to bank clerks as tellers, but most of use are not aware of the history behind why we do this. In some ways, the phrase "bank teller" is a fossil, a word whose original contextual meaning has faded from memory. Today people apply a modern interpretation of the phrase's meaning that is close but not exactly the same as the original medieval definition, much in the way that scientists try to interpret fossils of animals and plants.
Other Uses of Teller
Another example of the original meaning of the word teller, "one who counts" is its use in the United Kingdom in political elections. In this context, a teller is a vote counter.