Step 1: Recall the naming rules. To name an alkane we find the longest continuous carbon chain, number it so substituents get the lowest set of locants, and list substituents alphabetically. Step 2: Find the parent chain. The longest chain in this hydrocarbon contains $8$ carbons, so the parent is octane. Step 3: Place the branches. There are three methyl branches on this octane chain. We must number to keep their positions as small as possible. Step 4: Choose the numbering direction. Numbering from one end gives methyls at $2, 5, 6$; numbering from the other end gives $3, 4, 7$. Comparing the sets, $\{2,5,6\}$ is lower at the first point of difference. Step 5: Write the substituent prefix. Three identical methyls give the prefix trimethyl, located at $2, 5, 6$. Step 6: Assemble the name. Combining, the IUPAC name is 2, 5, 6-Trimethyloctane, which is option 1. \[ \boxed{2, 5, 6\text{-Trimethyloctane}} \]
