Resources for Kesubos daf 11
1. The גמרא says that you can be מגייר a non-Jewish child על בית ב"ד. There are many questions to address with this process:
1.1. First, who is bringing this child to ב"ד? The ריטב"א quotes רש"י as saying that the child is being brought by both of his parents, but the ריטב"א adds that if the child had his own דעת and came on his own we would be מגייר him as well. The only thing we would not do is be מגייר a child who was not being brought by his parents and did not have his own דעת. (The גירסא we have in רש"י says that the case of גר קטן is where the mother brought the child and the father was not around. Nonetheless, the יעב"ץ says רש"י is לאו דוקא.) Interestingly, the בה"ג is quoted by the טור in סימן רס"ח as saying that if the parents don’t bring the child and the child only comes on his own we will not accept the child for גירות. On the other extreme, the תוספות רי"ד says that we would even be מגייר an abandoned child left on the street.
1.2. The second question is the fact that at least when the child is young there is no קבלת המצוות whatsoever. How can you have a גירות without קבלת המצוות? The ריטב"א in ד"ה והאי says something rather shocking: he says הודעת המצוות is not מעכב the גירות at all. Theרמב"ם in הלכות איסורי ביאה פּרק י"ג הל׳ י"ז says this as well. This would seem to be against תוספות in יבמות דף מ"ה ע"ב ד"ה מי who says that it is מעכב. It also seems to be counterintuitive. The תשובות חמדת שלמה in סימן כ"ט (brought in the פּתחי תשובה in סימן רס"ח) suggests that there is a difference between קבלת מצוות and הודעת מצוות. Telling the גר some of the מצוות and the שכר ועונש associated with them is not מעכב. (Along the same vain, the יעב"ץ says that telling the גר the חומר המצוות is only necessary for an adult who was טועם טעם חטא but not for a child.) However, the general קבלת המצוות is מעכב. While this would minimize the מחלוקת רמב"ם ותוספות, it doesn’t explain how גירות could work by a child where there isn’t even a general קבלת המצוות. The ברכת שמואל in קידושין סימן ט"ו explains based on תוספות in סנהדרין דף ס"ח that קבלת המצוות is not מעכב at the time of the גירות of the child since it isn’t an inherent part of the act of מילה וטבילה itself. Rather, it is just a מעכב to the גירות being חל. Therefore, since a child isn’t capable of קבלת מצוות, it’s not מעכב for now. Once a child becomes a גדול it becomes מעכב again and when the child isn’t מוחה it counts as a קבלה.
1.3. The final issue is whether the גירות of a child is חל מדאורייתא or only מדרבנן. רש"י in ד"ה על דעת ב"ד says that once he becomes a גר he can touch wine. The פּני יהושע points out that that touching wine is only a דין דרבנן and רש"י must hold its only a גירות מדרבנן. The ריטב"א also brings those that hold that it must be דרבנן or else we couldn’t rely on the גירות at all since the child may be מוחה when he gets older. The ריטב"א disagrees with this שיטה and says that if the kid is raised as a frum Jew we don’t need to be חושש he will be מוחה at age 13 even if it is a גירות דאורייתא since it isn’t שכיח.
1.4. As to the practical side of this הלכה, Rav Moshe ז"ל in אגרות משה יו"ד חלק א סימן קס"א discusses the procedure of גירות for parents who adopt non Jewish children. While the bris is done immediately, the טבילה needs to wait till the child is old enough to be dunked (around two years old). Therefore, we don’t not have a קריאת השם until the טבילה is completed. At that time the name can be whatever the adoptive parents choose and you can call him בן the adoptive father if the adoptive father wants since he is also considered his son.