I am looking for the terminology that I can use in order to find one of these clamps to buy online. I can mount it on wood and then tighten it to keep a pipe in place.
Pipe grip tie is the term used by Simpson for PGT® Pipe Grip Ties® which are used to attach a wood fence to a metal pipe support.
To tell the truth that looks home made to me but it is a pipe strap / clamp. Pro’ s usually use strut clamps , like kindorf, uni strut or power strut. I said home made because of the hole on the top under the bolt, the strap is not flat to the surface on the bottom. I would use 1/2” strut channel and an appropriate rigid or universal clamp. We use these in very large numbers in industry but some residential sparky’s save a few $$$ and bend them out of metal strapping. Your example is better than plumbers tape ... galvanized strip with holes ... used in a loop or similar manner.