Ken Thompson worked with BCPL on the Multics project, so when he started working on a new operating system called Unix, he was inspired by that language in creating his own new programming language for use in that project, which he called B (apparently after the first letter of the predecessor language). While BCPL was already designed to be efficient in resource use, Thompson slimmed down B even more, so it would work in the very low-resource small computers he was targeting. B had only one data type, the 'word', which could represent a number or an ASCII character.
The syntax was greatly changed from BCPL, and includes much that would look at least vaguely familiar to modern programmers used to C and its descendants. As B was revised and expanded during the development of Unix, eventually it had acquired sufficient new functionality to deserve a new name, and this is when C was born.