Was Galileo mentioned by the participants of the Second Vatican Council?
Yes, during the first half alone he was mentioned explicitly by name three times:
Attendite, venerabiles Patres, ad conditionem eorum omnium, qui cum fide catholica componere debent scientificum laborem in universitatibus, in omnibus scientiarum circulis. Exemplum Galilaei et alia exempla recentiora sufficiant! Immaturae declarationes alicuius Concilii, propter earum solemnitatem, onerare possent, dicamus in semisaeculum, conditionem scientificorum.
[Beware, venerable Fathers, of the condition of all those who with catholic faith must compose scientific work in the universities, in all scientific circles. Let Galileo and the other more recent examples suffice! The immature declarations of some in this Council, because of their solemnity, could aggravate—we speak in the mid-century—the condition of the sciences.]
Bp. emeritus of Innsbruck, Austria, Paulus Rusch (1903-1986) explicitly mentioned Galileo during the 22nd meeting, 19 Nov. 1962, in his intervention (p. 356-357) against ch. 2, #12 ("Inerrancy") of the first schema the fathers voted on: De fontibus revelationis. Cdl. Siri's intervention, which mentioned Pope St. Pius X and Modernism, is on p. 38-39. The very next day, 61% of the council fathers rejected the schema (cf. Ratzinger Reader pp. 258 ff.). John XXIII thereafter called upon a mixed commission (incl. Cdl. Frings, whom Fr. Ratzinger advised, and Rahner) to redraft it. Cdl. Frings said (p. 34-35) the original schema was too scholastic and professorial in tone, "nec aedificans nec vivificans" ("neither edifying nor vivifying")!
Here is De fontibus revelationis ch.2, #12 on inerrancy:
Because divine Inspiration extends to everything, the absolute immunity of all Holy Scripture from error [PTC had said "the infallibility and inerrancy"] follows directly and necessarily. For we are taught by the ancient and constant faith of the Church that it is utterly forbidden to grant that the sacred author himself has erred, since divine Inspiration of itself as necessarily excludes and repels any error in any matter, religious or profane, as it is necessary to say that God, the supreme Truth, is never the author of any error whatever. [Pius XII, Divino afflante (EB 539), using the words of Leo XIII, Providentissimus Deus (D 1950); see also EB 44, 46, 125, 420, 463, etc.]
Accedit nostram Ecclesiam hac in re iam duram passam esse experientiam. Anno 1633 Galilei sub Urbano VIII damnatus est, quia defendit doctrinam contra Scripturam. Doctrinam autem quam defendit erat, sicut notissimum est, terram circa solem rotare et non viceversa.
[Additionally, our church has already suffered a hard experience in this matter. In 1633 Galileo was condemned under Urban VIII because he defended a doctrine contrary to Scripture. But the doctrine that he defended was, as is well-known, that the earth revolves around the sun and not vice versa.]
Bp. Michel Darmancier (1918-1984), titular of Augurus, commenting on the "De ecclesiæ magistero" section (p. 47-54) of the 23 Nov. 1962 schema De ecclesia (p. 12 ff.), wrote in his "written animadversion" (p. 452):
De illis enim contingentibus elementis sicut in fide et theologia proprie dicta consentire possunt theologi per saecula et per totum orbem catholicum, illa intimius coniungentes cum dogmatibus, quin exinde oriatur quaevis certitudo de illorum veritate, etsi concludi potest fidem ex illis detrimentum non timere. Sic, usque ad saeculum XVI, unanimiter docuerunt theologi terram centrum universorum esse, unde Galileus quidam satis notas difficultates cum sancta Inquisitione expertus est.
[The theologians can agree, throughout the ages and the whole catholic world, on those contingent elements in faith and theology properly speaking which are intimately connected with dogmas, which might not arise from any certainty of their truth, although to fear a loss of faith from them cannot be concluded. Thus, until the 16th century, theologians unanimously taught that the earth was the center of the universe, whence Galileo experienced some well-known difficulties with the holy Inquisition.]
See also the article on Galileo at Vatican II in this book.