Al-Baqī The Everlasting,The Eternal is one of the 99 names of Allah [1] :

- The Everlasting, The Eternal, The Ever-Enduring, The Ever-Present

- The One who has always existed and who will never cease to be.

- The One whose existence has neither beginning nor end.

- The One whose existence is beyond the realm of time.

- The One who existed before all of creation, and who will remain after all of this creation has come and gone.

- The One who is everlasting, perpetual, beginning-less, endless. The One whose existence is eternal.

- The One who remains forever, unaffected by time.

From the root b-q-y which has the following classical Arabic connotations:

to remain, continue, endure
to be permanent, everlasting, constant
to survive forever
to be incessant, continuous, endless

The term Bāqī is not specifically used as a Beautiful Name in the Qur'ān.

The term Abqā, also from the b-q-y root, is used in the Qur'ān (20:73) where it is commonly translated as the Most Lasting, Ever Lasting or Most Abiding.

{ We have had iman in our Lord so that He may forgive us for our mistakes and for the magic which you forced us to perform. Allah is better and longer lasting }
Qur'ān (20:73)

The term baqiyyah is used in the Qur'ān (11:116) to describe persons of excellence, those who possess spiritual understanding and inner discrimination, those who possess a quality of attending to that which is eternal.

The related term baqā', which is from the same b-q-y root, is often translated as eternal life. In the state of baqā' bi-llāh there is a return from the ephemeral to the eternal, a shift from the egocentric to the Divine, where all that remains is the eternal Thou. The return to the Everlasting, the return from one's worldly preoccupation with the ephemeral, the shift away from one's own ego being treated as the center of life, is often called fanā' which literally means to fade away, dwindle, recede or come to an end.

yā bāqī anta al-bāqī is a powerful wazīfa which can be translated as o' Everlasting One, Thou art The Everlasting One.

[1] : read the 99 names of Allah