Yes, it is a name, short for William, though I’m not sure how Bill was derived from William.
As you know, like many words this one has a number of other meanings, like,
A bird has a bill, particularly those birds with webbed feet
A bill is something you are sent to pay for goods or services, and often turn up when least expected, or when money is tight
And, sadly, they are neverending.
Then there’s fit the bill, which means it is suitable.
It could also be a list of people who appear in a programme.
It is used to describe banknotes, such as a twenty dollar bill.
It could be a waybill, used for the consignment of goods.
It could also be a piece of legislation introduced into parliament.
In some places in the world, it could be the peak of a cap
But the most obscure use of the word bill goes to: the point of an anchor fluke.