The name plate on the time machine usually reads WABAC, but it reads WAYBAC on occasion.
Many of the depicted historical figures bear little resemblance to the real people. However, Peabody does explain in Show Opening (1959) that WABAC is not really a time machine, but a should-have-been machine. It is a gateway to a sanitized idealistic version of history. E.g., this explains why everybody they meet speaks American English.
The settings of many adventures are full of anachronisms, which are not explained away as part of the time traveling action.