Once I had the relevent death certificates, I checked through the Witton Cemetery burial registers at Birmingham Central Library for matches around the dates shown on the death certificates. Once I had a match or matches I noted the burial reference number/s and presented that at the cemetery office. That coupled with the date, enabled them to give me plot and section numbers and information such as the last known address and on the odd rare occasion the purchaser of the burial rights. It was these last two pieces of information that "clinched" it for me when I had a couple of possible matches, when a couple of people with the same name died at around the same time.
Did you contact the cemetery first and ask for a broad search between two dates, then get the certificates or as I did?
Either way, with "several years difference" in one case, it looks like one of the graves or one of the certificates is not the one you are looking for, even with a name that is not that common.
