To my knowledge the suggestion that stars are other suns was not made during ancient times (there are claims attributed to Democritus and Epicurus, but those can be interpreted in many ways).

The English mathematician and astronomer Thomas Digges (1546–1595) was the first to expand the Copernican model with an infinite space scattered with stars. Of this infinite space he writes in a figure:

This orb of stars fixed infinitely up extends itself in altitude spherically, and therefore immovable the palace of felicity garnished with perpetual shining glorious lights innumerable, far excelling over [the sun] both in quantity and quality the very court of celestial angels, devoid of grief and replenished with perfect endless joy, the habitacle for the elect.

Now if this is not explicit enough for you the Italian friar Giordano Bruno (1548–1600) who was burned at the stake for his heritical writings, states in his On the Infinite Universe and Worlds:

There are countless suns and countless earths all rotating round their suns in exactly the same way as the seven planets of our system. We see only the suns because they are the largest bodies and are luminous, but their planets remain invisible to us because they are smaller and non-luminous. The countless worlds in the universe are no worse and no less inhabited than our earth. For it is utterly unreasonable to suppose that those teeming worlds which are as magnificent as our own, perhaps more so, and which enjoy the fructifying rays of a sun just as we do, should be uninhabited and should not bear similar or even more perfect inhabitants than our earth. The unnumbered worlds in the universe are all similar in form and rank and subject to the same forces and the same laws. (taken from wikiquote, who list it as: As quoted in The Discovery of Nature (1965), by Albert W. Bettex.)

Now it should be noted that Bruno was no astronomer and most of his work is of a theological nature, see here for a nice (dismissive) essay on his importance:

There is nothing in [Bruno's] writings that contributed to our knowledge of astronomy in any substantial way, and indeed his astronomical writings reveal a poor grasp of the subject on several important points.

It was only in the 17th century of Newton that the notion of stars as other suns become common among astronomers.