So, how does Congress decide on the final name of the bill?
Same as with every other provision. They debate and amend it in committee, chamber, or by joint action. So assuming that the Senate bill is based on the House bill and they already made that change, they had a vote to replace one version with another version and one effect of that was to change the name.
In this particular case, they may not have had that vote yet. Remember that the current health care bill is a draft bill. It has not gone through the amending process as far as I know. So they will eventually have a vote on replacing the entirety of some House bill with the Senate version of the health care bill. But to this point, they are probably still just proposing to make changes in the bill. That's why it is a draft.
Anyway, to get back to the question, changing the name is the same as changing any other word in the bill. They amend it via a vote somewhere.