Did Protestants of 17th Century, refer to themselves as Protestants?

Yes, but probably not in the way you're thinking.

I'm thinking in particular of the original English American colonists, did they act in the name of their King and 'Protestantism'?

They acted in the name of their King to some degree, as the head of the English government, but they did not particularly act in the name of "Protestantism".

To explain:

Yes, there was a group in England in the 1600s that called themselves "Protestants". But, no, they were not the group of English colonists who came over to America in the 1600s for political/religious reasons. Those were the "Puritans" and they called themselves the "Puritans". It's not a later term that was applied to them retroactively. They would have referred to themselves as "Puritans" and not "Protestants" and they would have made that very distinction.

To put it more plainly:

There was the Catholic Church, and then there was the Reformation on the European continent. The German and Dutch speakers who followed Martin Luther out the door of the Catholic Church called themselves "Protestants".

This word came into English and was used by supporters of Henry VIII as the Church of England began to break away from the Catholic Church in the mid-1500s.

But there came a political/religious movement (politics and religion being nearly one and the same back then) who thought that the "Protestant" movement in England didn't go far enough, and that the Church of England still remained too close to the Catholic Church.

This wing of politics and religion in England in the late 1500s and early 1600s called themselves the "Puritans" and considered themselves distinct from the royalist "Protestants", both of whom considered themselves distinct from the pro-Catholic Church "Papists".

On the royalist/Protestant side, they did not use the word "Puritan" to describe their political foes. They instead called them the "Dissenters" or "Separatists" who wanted a wider separation between the Church of England and the Catholic Church, and thought the King of England still had too much power over the church.

The colonists in Plymouth, then, would have called themselves "Puritans". There were surely some "Protestants" who came to New England not long after the Mayflower, and Virginia had started out with "Protestant" colonists as well. Certainly, there were far fewer "Puritans" among them down in Virginia.

Back in England, when the English Civil War broke out in the 1640s, many English-Americans would have viewed it as a conflict between Puritans under Oliver Cromwell, and Protestants who supported King Charles.

After the Restoration in 1660, the Puritan movement died out, and with it, so did the word "Puritan" to describe a religious or political group. There remained "Papist" and "Protestant" factions in politics, but as the 1600s came to an end and the 1700s came on, these distinctions became less about politics and more about religious affiliation. Particularly in America, by the time of the Revolution, the country was populated by Catholics, Episcopalians (Church of England), Presbyterians (Church of Scotland), the Dutch Reformed Church, the Lutheran Church, the Quakers, the Anabaptists, and others. "Protestant" had by then lost most of its political meaning but retained the social meaning of "Christian that's not Catholic or Orthodox".

So, yes, there were colonists who came over to America who called themselves "Protestant", but, no there were not people coming over and founding colonies in the name of "Protestantism", particularly. The early Protestants who came over were people less interested in spreading religion and more interested in making money. The non-Catholic Christians who came over who were interested in founding a colony in the name of religion were the "Puritans", the political enemies of the group who considered themselves the "Protestants".

Sources:

Here are some 17th Century sources talking about Protestants, Puritans, and Papists: 1, 2, 3, 4

And here's a 1732 book called History of the Puritans which talks extensively about the political factions of Papists, Puritans, and Protestants, and how Queen Elizabeth I found a middle way reconciling the Papists and Puritans on either side of the political wing she represented, the Protestants.

And here are a few sources of the era displaying how the pro-royalists often called the "Puritans" by the name of the "Dissenters", "Separatists", or "Non-Comformists": 1, 2, 3

Further reading:

Papists, Protestants and Puritans 1559-1714 by Diane Newton, 1998