Butterflying a hot dog (or any similar sausage) has two effects.
First, as the moisture inside the hot dog expands during cooking, causing the casings to frequently burst due to the pressure that builds up.
When you butterfly a hot dog the this is prevented.
Such blistering does not 'harm' the hot dog but are somewhat 'unsightly',
so I would call this an aesthetic effect.
The second effect is that it allows the hot dog to cook through more evenly.
Particularly for those who prefer their hot dog well done butterflying can get the insides cook through without charring the outside.
[Edit: found something interesting to add...
]If
you want to impress your friend with something different,
try spiral cutting your hot dog .
cooking.stackexchange.com/users/6279/Cos Callis
Butterflying also exposes a greater area of the surface to the grill's direct heat, leading to browning and smoky flavor.
cooking.stackexchange.com/users/9842/Trey
Butterflying a hot dog or sausage increases the surface area available for the Maillard reaction (all the awesome taste sensations that come from browning and burning.
It also decreases cooking time and allows for more even cooking; a thick sausage cooked whole will often be dry on the outside in order to get it fully cooked at the center.
The trick to effective butterflying is to put the open side down on a hot pan (a bit above medium will usually do it) for a minute or two.
Do not press down as you’ll lose juices.
Flip the sausage or hot dog and lower the heat to a little below medium.
You’ll see juices rise to the top like when you cook a burger.
Again, do not press down and lose the juices.
Total cooking time should be less than usual.
When you take it off, place it flayed side up on a dish and let it sit for 3-5 minutes so any juices soak into the meat and aren’t lost to the plate when cutting.
Enjoy the lovely burnt/browned umami!
cooking.stackexchange.com/users/75331/Sarasota Joe
Some people slice hot dogs lengthwise in an effort to make them a little safer for children.
Hot dogs are a choking hazard for kids , so the idea is to make the pieces in each bite smaller and easier to chew.
I don't know of any research that demonstrates that slicing lengthwise is effective, but since pediatricians recommend cutting hot dogs into small pieces for little kids, it seems a step in the right direction even for not-quite-so-little kids.
cooking.stackexchange.com/users/5505/Caleb
For quicker cooking or to for on tost.
Just don't cook to long.
You also can put a piece of cheddar down the middle.
cooking.stackexchange.com/users/72881/Just jude
A friend of mine butterfly cuts (in half lengthwise without separating) his hebrew national hot dogs before grilling them.  I don't notice a difference in flavor and didn't perceive a decrease in required grill time. Is there anything gained by butter flying a hot dog for grilling?
Is there anything gained by butterfly cutting a hot dog for grilling?
cooking.stackexchange.com
<grilling><cutting><hot-dog>
cooking.stackexchange.com/questions/24486
cooking.stackexchange.com/users/809/ahsteele
This increases the surface area for browning, stops the hot dogs from bursting, helps the hot dogs to cook more evenly and reduces the choking risk for children. Slicing them prevents them from bursting and makes them easier for children to eat. It also helps them to cook more quickly.
Slicing the hotdog prevents the hotdog from bursting. It should allow it to cook through more quickly. Slicing them lengthwise makes them easier for children to eat.