For methyl-butan-2-ol does it matter how the displayed formula is drawn?

Option 1:

-------OH
---------I
CH3 - C - CH2 - CH3
---------I
-------CH3

Option 2:

-------CH3
---------I
CH3 - C - CH2 - CH3
---------I
-------OH

I saw some websites that had the structure drawn like option 1 and some websites that had the structure drawn like option 2.

I'm struggling with the name. You have drawn both structures properly for 2-methylbutan-2-ol; i.e., in your post there is no indication in the name where the methyl group is attached. Both structures are the same.