If someone as a baby had a bris done by a mohel but feels he still has foreskin going over his glans, then does he need another bris or has he fulfilled his obligation?
In short, sometimes another milah is required, and sometimes not -- it depends on how much skin is left over.
The Mishna says (Shabbos 19:6):
אֵלּוּ הֵן צִיצִין הַמְעַכְּבִין אֶת הַמִּילָה, בָּשָׂר הַחוֹפֶה אֶת רֹב הָעֲטָרָה. וְאֵינוֹ אוֹכֵל בַּתְּרוּמָה. וְאִם הָיָה בַעַל בָּשָׂר, מְתַקְּנוֹ מִפְּנֵי מַרְאִית הָעָיִן. מָל וְלֹא פָרַע אֶת הַמִּילָה, כְּאִלּוּ לֹא מָל:
These are the excrescences [knobs] which impede the circumcision; flesh which covers the greater part of the gland: [such an one if a priest] must not eat of heave-offering (תרומה). If [this arise because] a man becomes very fleshy, it must be remedied, for the sake of outward appearance. If he has circumcised, but not uncovered the gland, it is as if he had not circumcised at all.
( slightly modified from the linked Sefaria translation )
This is brought down by Shulchan Aruch, Yoreh De'ah 266:2:
מִילָה דּוֹחָה יוֹם טוֹב וְשַׁבָּת, בִּזְמַנָּהּ. אֲבָל שֶׁלֹּא בִּזְמַנָּהּ, אֵינָהּ דּוֹחָה. וַאֲפִלּוּ בִּזְמַנָּהּ, אֵינָהּ דּוֹחָה אֶלָּא הַמִּילָה עַצְמָהּ וּפְרִיעָה וּמְצִיצָה, וַאֲפִלּוּ פֵּרַשׁ, חוֹזֵר עַל צִיצִין הַמְּעַכְּבִין דְּהַיְנוּ אִם נִשְׁאַר מֵהָעוֹר עוֹר הַחוֹפֶה רֹב גָּבְהָהּ שֶׁל עֲטָרָה אֲפִלּוּ בְּמָקוֹם אֶחָד. וְעַל שֶׁאֵינָם מְעַכְּבִים, אִם לֹא פֵּרַשׁ, חוֹזֵר, וְאִם פֵּרַשׁ, אֵינוֹ חוֹזֵר.
Milah is done on Shabbos and Yom Tov, provided that that's the eighth day. If it's not the eighth day, then milah is not done on Shabbos or Yom Tov. And even on the eighth day, the only thing that is done is the actual milah, together with the priya (peeling back the skin) and the metzitzah (drawing out blood). Even if the mohel stopped, he goes back for the parts that disqualify the milah, such as if there is leftover skin that covers most of the "crown" (glans) along its height, even in one place. even the pieces that do not disqualify the milah, if the mohel didn't stop, he goes back and gets them; if he did stop, then he does not go back to get them.
( translation mine )
I knew this from learning that part of Maseches Shabbos a while ago; I did cursory searches around Shas, Shulchan Aruch, and Mishneh Torah, and didn't find anything that spoke directly about the case you asked about. However, I would make the simple argument that if we violate Shabbos for ציצין המעכבין, those parts that disqualify, even if the mohel already stopped, it's very easy to say that we would certainly go back for those parts after Shabbos. However, there is still an amount (עוֹר הַחוֹפֶה רֹב גָּבְהָהּ שֶׁל עֲטָרָה, skin that covers most of the height of the "crown") that's okay to leave on, and wouldn't require a second bris milah.
Of course, if you have any reason to believe that this has practical ramifications, you should ask a rabbi or professional mohel who will be able to give advice based on the specifics of the case, as I don't doubt that this is a little bit more complicated than what I wrote here.
( Hebrew texts copied from Torat Emet 357 )
With all due respect to @shokhet(+1).
even if most of the glans are not covered if most of the circumference of the corona glandis is covered it also is not a bris
as can be seen in @Kouty's here under 1 in the number list
If residues of foreskin remain, have we to cut them? The Shulchan Aruch says in Yore Dea siman 264, se'if 5, that if in some place a residue of foreskin covers the majority of the length of the glans, even in a small area, he still needs to circumcise as if he was not circumcised. The Baer Heytev (in name of an opinion reported in Bet Yosef and Shach) adds that if the majority of the circumference of the corona glandis is covered, he is not regarded as circumcised. This part of the inspection may be a self inspection
and in Aruch Hashulhan Y"D 264.21