Bukhari

Hadith Commentary:
The use of the word "Rabb" (Lord) has been prohibited.
Similarly, the use of "abd" (male servant) or "amah" (female servant) has been discouraged so that there is no suspicion of shirk (associating partners with Allah), although saying so is disliked (makruh), not forbidden (haram), as is mentioned in the Qur'an: ﴿اذْكُرْنِي عِندَ رَبِّكَ﴾ (Yusuf 12:42) .
Some have said that it is prohibited to call out in this manner when invoking.
In short, when the figurative meaning is intended, at most this act will be considered disliked (makruh), and this is the reason why the scholars have regarded it as disliked to keep names such as "Abd al-Nabi" (servant of the Prophet) or "Abd al-Husayn" (servant of Husayn), and have described keeping such names as shirk in the sense that they contain the implication or suspicion of shirk.
If the literal meaning is intended, then without doubt it is shirk.
If the figurative meaning is intended, then it will not be shirk, but there is no doubt regarding its being disliked (makruh); therefore, it is better not to keep such names.
Because wherever there is a suspicion of shirk, it is always better to avoid it.
Especially the word "abd" (servant) is such that its attribution is only appropriate towards the word Allah, or al-Rahman, or al-Rahim, and other beautiful names (asma’ al-husna) of Allah.
It is incumbent upon the followers of tawhid (monotheism) and sunnah that they never attribute their servitude (ubudiyyah) to other than Allah.
This is precisely what "iyyaka na’budu" (You alone we worship) demands.
And Allah is the One who grants success.

Hadith Commentary:
(1)
The use of this word is prohibited because true Lordship (rububiyyah) is only befitting to Allah; therefore, this word should not be used for any of the creation. However, in the Noble Qur’an, this word has been used for other than Allah with an addition (idafah), as in: ﴿اذْكُرْنِي عِندَ رَبِّكَ﴾ (Yusuf 12:42) , from which it is understood that the prohibition in the hadith is not one of absolute unlawfulness (tahrimi). And Allah knows best.

(2)
Imam Nawawi rahimahullah has written that if the words “my slave” (abdi) and “my slave-girl” (amati) are used with bad manners and arrogance, then their use is disliked (makruh), and if only praise is intended, then there is no harm in saying these words. (Fath al-Bari: 5/223) In any case, the master should avoid pride and arrogance when calling his male or female slave, and likewise, the slave should also avoid using such words for his master that express reverence similar to that due to Allah.

Hadith Commentary:
Vocabulary of the Hadith:
‘Ubayd:
Plural of ‘abd,
servant,
ama’,
plural of amat,
female slave.

Benefits and Issues:
The purpose of the hadith is to save a person from falling into arrogance, pride, and conceit, and to instill within him humility, modesty, and a sense of neediness before Allah. Therefore, the use of such words has been prohibited that may create in a person a sense of superiority and preeminence, as a result of which arrogance, pride, or self-admiration may arise within him. For this reason, a person should not refer to his male or female slave as “my slave” or “my bondwoman.” However, the slave or bondwoman themselves may say, “ana ‘abduka” (I am your slave), “ana amatuka” (I am your bondwoman), and others may say, “‘abduka amatuka” (your slave, your bondwoman).