The strained yogurt dip described in the question is labneh, a Lebanese staple often finished with olive oil and za'atar.
Labneh is made by straining yogurt to remove whey, producing a thick, creamy texture between yogurt and soft cheese. It is commonly served cold as part of a mezze spread or at breakfast, with flatbread, olives, mint, and vegetables.
Its name has several spellings, including labaneh, labna, and labni, reflecting Arabic dialects and transliteration choices. The dish is widespread across the Levant, not exclusively Lebanon, and similar strained-yogurt foods exist elsewhere in the Middle East and Mediterranean.
Labneh is sometimes confused with Greek yogurt. Greek yogurt is also strained, but labneh is typically thicker and more distinctly associated with Levantine cuisine. Drier labneh can be shaped into balls and preserved in olive oil.