Like most old family recipes, there are multiple stories behind this one. Bayne comes from a young cousin, many years ago, being unable to pronounce Grandmother Payne. Instead it came out Bayne (or Bane). From then on it just stuck and Grandmother Payne was called Bayne by all the grandkids.
The pudding gets its name from another spoiled cousin (we were all spoiled rotten - the family didn't have much but they happily gave what they had to appease the kids). This little cousin loved chocolate pudding and "asked" for it regularly. One day Bayne was in a hurry and made instant pudding. That didn't work at all for little cousin. Next time little cousin demanded...um, I mean asked, for pudding she said "I want the one where you take your time." From then on the chocolate pudding was Bayne's Take Your Time Pudding.
Now, while I come from a long line of tall tale telling folks, I am not exaggerating in the least to say that this pudding was the cause of more than one "heated discussion" between family members who normally loved each other very much but were determined to get the last bit of pudding in the bowl.
So, take your time making the pudding and take your time enjoying the rich chocolatey goodness!