The King's Men.
Shakespeare became one of the founding members of the Lord Chamberlain's Men company.
He became their patron.
Lord Hunsdon's Men became the Lord Chamberlain's Men which became the King's Men.
They didn't change their name--it was changed for them when their patron changed or when his job changed. In fact their name changed several times: From the Lord Chamberlain's Men to Lord Hunsdon's Men when the Lord Chamberlain died and his son Lord Hunsdon took over patronage of the company, from Lord Hunsdon's Men to the Lord Chamberlain's Men when Hunsdon became Lord Chamberlain like his father, and from the Lord Chamberlain's Men to The King's Men when King James I took over patronage of the company. The partners in the company had nothing to say about it.
The Lord Chamberlain's Men became The King's Men.
In 1603, The Lord Chamberlain's Men became The King's Men.
The Lord Chamberlain's Men became The King's Men in 1603.
Lord Chamberlain's Men was created in 1594.
Shakespeare was co-owner of The Lord Chamberlain's Men which briefly became Lord Hunsdon's Men when their original patron died, but his son was also made Lord Chamberlain and so they resumed the first name. in 160, it became the King's Men. the company had three names, but it was only one company.
He joined the Lord Chamberlain's Men in 1594. He was a charter member.
Shakespeare was an actor and playwright in the Lord Chamberlain's Men who later became the King's Men. He was not in the Lord Admiral's Men.
Lord Hunsdon, the Lord Chamberlain of England, was the company's first patron. When he died his son became their patron and, coincidentally, was also made the Lord Chamberlain. In 1603, the company took the title of its new patron and became the King's Men.