What is the name of this type of inflorescence?
That is a woody compound umbel. A compound umbel is one with more than one set of pedicels between the peduncle and the flower. Hydrangeas also exhibit this type of inflorescence, although not necessarily woody.

In the picture below, I've marked all the levels where the pedicels branch.


End of peduncle, beginning of primary pedicels
Beginning of secondary pedicels
Beginning of tertiary pedicels
Beginning of quaternary pedicels, which bear flowers