I have been looking in Shaykh ibn Uthaymeen’s Al-Qawaa‘id Al-Muthlaa to find the name Al-Badee‘, but I could not find it. However, in surat Al-Baqarah 2:117 "Badee‘ (Originator) of the heavens and the earth. When He decrees a matter, He only says to it, “Be,” and it is" Ibn Kathir mentioned in his Tafseer (Quran exegesis) (The Badee‘ [Originator] of the heavens and the earth.) which means, He created them when nothing resembling them existed.
Can any one confirm me about the authenticity of this name? May Allah reward you. I heard that the Arabic word بَدِيعُ is used to describe creation from nothing and that the Arabic word خلق is used to describe creation from something that is already present.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ʻalayhi wa sallam, is His slave and Messenger.

The name Al-Badee‘ (the Originator) was mentioned as one of the Names of Allah in the hadeeth narrated by Abu Hurayrah, may Allah be pleased with him, in which the Prophet, sallallahu ʻalayhi wa sallam, said, “Allah has ninety-nine names; one hundred less one, for He is Witr (One, which is an odd number) and He loves Witr. Whoever learns them will enter Paradise. Huwa Allahu, La Ilaaha Illa Huwa (He is Allah, the one and only God worthy of worship), Ar-Rahmaan, Ar-Raheem ... Al-Badee‘, Al-Baaqi, Al-Waarith, Ar-Rasheed, As-Saboor...” [At-Tirmithi and Ibn Hibban]

It is known that scholars declared this hadeeth's chain of narration to be weak, and they underlined that the hadeeth was reported to be authentic without the part that lists the names. Some scholars considered the name Al-Badee‘ to be one of the Names of Allah:

Al-Haafith Ibn Hajar said in his book Fat-h Al-Baari, “Al-Badee‘ is one of the Names of Allah...”

Ibn Al-Atheer said in An-Nihaayah about the Names of Allah, “Al-Badee‘ is the Creator and Innovator who originate something without a prior example...”

Ibn Manthoor said in Al-Lisaan, “Al-Badee‘ (Originator) is one of the divine names of Allah becauses He originates things and brings them into existence...”

Abu Mansoor Al-Azhari said in Tahtheeb Al-Lughah, “Badee‘ is one of the Names of Allah, and He is Al-Badee‘...”

We have previously underlined in fatwa no. 57265 in our Arabic section that we believe that we give more weight to the view that it is not one of the Names of Allah because it was not mentioned except in the genitive case (Badee‘ As-Samaawaat, meaning Originator of the heavens).

Allah knows best.