Dfyjkt

In the Talmud, I think it is in berachos, there is mentioned a group of extremely pious people. Does anyone know the name of this group?

There is not much information in the question to go on, so this is hardly a definitive answer, but perhaps you are referring to the following:

Berachot 9b

העיד ר"י בן אליקים משום קהלא קדישא דבירושלים כל הסומך גאולה לתפלה אינו
נזוק כל היום כולו

R. Jose b. Eliakim testified in the name of the holy community of
Jerusalem: If one joins the ge'ullah to the tefillah, he will not meet
with any mishap for the whole of the day. (Soncino translation)

Thus, the group is called קהלא קדישא דבירושלים, or The Holy Community of Jerusalem.

There is another group mentioned on the same page:

אמר אביי לתפילין כאחרים לק"ש כותיקין דאמר ר' יוחנן ותיקין היו גומרין
אותה עם הנץ החמה תניא נמי הכי ותיקין היו גומרין אותה עם הנץ החמה כדי
שיסמוך גאולה לתפלה ונמצא מתפלל ביום

Abaye says: In regard to the tefillin, the halachah is as stated by
the ‘Others’; in regard to [the recital of] the Shema’, as practised
by the watikin. For R. Johanan said: The watikin used to finish it
[the recital of the Shema’] with sunrise, in order to join the
ge'ullah with the tefillah, and say the tefillah in the daytime.
(Soncino translation)

Here the name of the group is ותיקין, or Watikin. It is not entirely clear who/what this refers to. Rashi explains it as referring to humble men to whom the commandment is dear:

אנשים ענוים ומחבבין מצוה

The footnote in the above translation states:

Lit., strong’ (sc.,in piety), a title probably applied to certain men
who, in the time of the Hasmonean kingdom, set an example of
exceptional piety. Some identify them with the Essenes.

Alternatively, you might be referring to the following:

Berachot 32b

תנו רבנן חסידים הראשונים היו שוהין שעה אחת ומתפללין שעה אחת וחוזרין
ושוהין שעה אחת וכי מאחר ששוהין תשע שעות ביום בתפלה תורתן היאך משתמרת
ומלאכתן היאך נעשית אלא מתוך שחסידים הם תורתם משתמרת ומלאכתן מתברכת

Our Rabbis taught: The pious men of old used to wait for an hour and
pray for an hour and then wait again for an hour. But seeing that they
spend nine hours a day over prayer, how is their knowledge of Torah
preserved and how is their work done? [The answer is] that because
they are pious, their Torah is preserved and their work is blessed.
(Soncino translation)

In this case the name of the group is חסידים הראשונים, or The Pious Men of Old.

Not in ברכות, but given the very vague parameters of the question, might it be the 36 hidden righteous mentioned in Sanhedrin 97b and Sukka 45b?

Abaye said: The world has no fewer than thirty-six righteous people in
each generation who greet the Divine Presence

A group of pious people called the "vatikin" (ותיקין) are mentioned on Berakhot 26a. As Rashi puts it, they are people who try extra hard to do mitzvot in their proper time, at the earliest possible.