Name for tombstone-holder parts?
Your terminology is correct: they're called tombstone (or bi-pin) fluorescent lampholders. In particular, those in the photo are locking or turn-type, a nice safety feature that makes it less likely for a lamp to fall out of the socket. A search at Amazon.com for Fluorescent Tombstone Lampholder found more than 30 similar devices.

N.B. There are two types, shorting and non-shorting, also called shunted and non-shunted. Be sure you examine your socket (you may need to pop off a plastic cover) and get the same type. Also, if you're converting from fluorescent to LED, check the type needed for the replacement tubes -- it might be different from your current lampholders.