Is it permissible for people to call themselves “Ahl al-Hadeeth”

Firstly: 

We are very happy to hear that you have become Muslim and
that you always pray in congregation in the mosque. We ask Allah, may He be
exalted, to increase you in guidance and steadfastness. 

Secondly: 

There is no reason why a group of Muslims should not call
themselves Ahl as-Sunnah or Ahl al-Hadeeth, or any other names that are
indicative of a Muslim’s sound methodology and following the Qur’an and
Sunnah, so as to distinguish themselves from others who follow innovation.
There is no doubt that the name Muslim is a good name, but… Unfortunately
the Muslims have divided into various groups, so that one may be Sufi,
another may be Shi‘i, and another may be”rational”. 

Indeed, there are some who claim to belong to Islam but they
are not Muslims, such as the Baha’is and Barelvis. 

If a Muslim describes himself as belonging to Ahl al-Hadeeth,
that means that he is disassociating himself from these groups and declaring
that he belongs to Ahl as-Sunnah wa’l-Jamaa‘ah. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: 

There is no shame in declaring oneself to be a follower of
the salaf, belonging to it and feeling proud of it; rather that must be
accepted from him, according to scholarly consensus. The madhhab of the
salaf cannot be anything but true. If a person adheres to it inwardly and
outwardly, then he is like the believer who is following truth inwardly and
outwardly. If he adheres to it outwardly only, and not inwardly, then he is
like the hypocrite; he is to be accepted as he appears to be, and what is
hidden in his heart is left to Allah (to judge), because we are not
instructed to check on what is in people’s hearts.

End quote from Majmoo‘ al-Fataawa, 1/149 

Shaykh Saalih al-Fawzaan (may Allah preserve him) said: 

Calling oneself Salafi, if it is true, is fine and there is
nothing wrong with it. But if it is a mere claim, then it is not permissible
to call oneself a Salafi when one is not following the way of the salaf.

End quote from al-Ajwabah al-Mufeedah ‘ala As’ilah
al-Manaahij al-Jadeedah, p. 13 

It should be noted that calling themselves Ahl al-Hadeeth
does not mean that they do not follow the Qur’an. Perhaps this is the reason
why you are confused. Rather Ahl al-Hadeeth are those who follow both the
Qur’an and hadeeth; they are the ones who adhere to the guidance of the
Prophet (blessings and peace of Allah be upon him) and they are the ones who
follow the Companions of the Prophet (blessings and peace of Allah be upon
him) sincerely. Allah, may He be exalted, says (interpretation of the
meaning):

“And the first to
embrace Islam of the Muhajiroon (those who migrated from Makkah to Al-Madinah)
and the Ansaar (the citizens of Al-Madinah who helped and gave aid to the
Muhajiroon) and also those who followed them exactly (in Faith). Allah is
well-pleased with them as they are well-pleased with Him. He has prepared
for them Gardens under which rivers flow (Paradise), to dwell therein
forever. That is the supreme success”

[at-Tawbah 9:100]. 

Thirdly: 

Allah has bestowed upon you another great blessing after
guiding you to Islam, which is that you live among Ahl al-Hadeeth, Ahl
as-Sunnah wa’l-Jamaa‘ah. So strive to stay close to them, follow their
example and adhere to their way. 

See the answer to question no.
159436 for a brief discussion on
Jamaa‘at Ahl al-Hadeeth in India, so that you will be more keen to stay
close to them. 

See the answer to question no.
12761 for further discussion on
the terminology “Ahl al-Hadeeth” among the righteous predecessors (as-salaf
as-saalih). 

And Allah knows best.