You need the category of 'no strong feeling either way ' - that 13.5% can't be added to either category as you suggest as it would be false. It is fully valid that a number of people don't mind if the names are changed or not.
Imagine if you had 100 people and the 'no strong feeling either way' actually accounted for 90 % for them. If these were excluded from the vote, you would then have a poll of just the remaining 10 people. If 6 of them them supported the idea and 4 were against, the poll would have the illusion of 60% in favour, 40% against.
But in reality, it would not reflect public opinion - adding those in the neutral category, the result would be 6% in favour, 4% against, 90% no strong feeling either way. A very different result.