I'm not sure I understand your question entirely. If there is only one possible message, then the ciphertext can be trivially decrypted simply by choosing this message.
I'll assume instead that the ciphertext contains the shuffled bit pattern of a name chosen from a set of more than one name. The problem with bit shuffling is that the number of set bits doesn't change. This significantly reduces the number of plaintexts that could correspond to a particular ciphertext.
For example, when the 200 most popular baby names of 2015 are written in uppercase ASCII, the number of set bits in these names is distributed as follows:
AVA is the only name that has 8 set bits, and even in the worst case of names that have 15 set bits, there are only 20 names to choose from (down from a total of 200). In other words, we can eliminate at least 90% of the possible plaintexts simply by counting the number of bits in the ciphertext.
If you use the same technique to encrypt more than one message, then you'll leak additional information about the exact permutation you're using. This will make the codebreaker's job even easier.