That's interesting. I've always thought the name a little weak, so you prompted me to find its origins. According to wiki:

Taler is short for the "Taxable Anonymous Libre Economic Reserves"[7][8] and alludes to the Taler coins in Germany during the Early Modern period.

That definitely looks like a backronym! Anyway, the wiki for the Taler coins says this:

The word is shortened from Joachimsthaler, the original thaler coin minted in Joachimsthal, Bohemia, from 1520.

So the original root appears to be Thal or Tal i.e. valley (just like Neanderthal/Neandertal). The Taler wiki page goes on:

[The Holy Roman Empire's] longest-lived coin was the Reichsthaler, which contained 1⁄9 Cologne Mark of fine silver (or 25.984 g), and which was issued in various versions from 1566 to 1875.

Was Denmark part of the Holy Roman Empire? Either way, your ancestors would've presumably often traded with Germans using these early Thaler/Taler coins.