both "have had" and "had had" are in perfect form / construction (i.e. present perfect and past perfect resspectively).
the present perfect tense is used when we want to connect the present with the past actions or experiences.
"I have had a terrible evening with my peers."
we use the Past Perfect to show that something started in the past and continued up until another action in the past.
"I had had a word with my boss about my promotion before I left the office."
also, "have had" and "had had" can be contracted as
've had = "I've had" "we've had"
'd had = "I'd had" "they'd had"
:)