All the beautiful names of Allah have a definite article prior to them:
Ar-Rahman الرحمان or الرحمن (The -most- gracious) not رحمن nor رحمان
Ar-Rahim الرحيم (The -most- merciful)
Al-Qayyum القيوم (The eternal)
Al-Wahid الواحد (The one)
Without this definite article it doesn't fulfill the condition of uniqueness which is necessary to be related to Allah!
Aahad آحاد (refers in Arabic to some singularity) or
Ahad أحد (the later means in Arabic somebody/someone)
Might be a bad choice as the related name of Allah is:
Al-Wahid al-Ahad الواحد الأحد (the one and only)
According the above the only correct name is:
And of course this name is permissible with the prefix "'abd" it is the name of a well known Andalusian hadith and fiqh scholar ibn 'Abd al-Barr ابن عبد البر.
The issue is that
In Arabic means compassionate/pious and similarly to this all names and attributes of Allah have a meaning, using them for naming without the prefix 'Abd or as an indefinite noun the meaning doesn't change significantly (except with the uniqueness) and that's why choosing such names is somewhat frowned upon due to ahadith about "praising oneself" like:
The Messenger of Allah (peace and blessings of Allah be upon him) said "The dearest phrases to Allah are four: Subhan Allah (Hallowed be Allah), Al-Hamdulillah (Praise be to Allah), La ilaha illa-Allah (There is no deity but Allah), Allahu Akbar (Allah is Greater). There is no harm for you in which of them begin with (while remembering Allah). And do not give these names to your servants: Yasar and Rabah and Najih and Aflah.
Do not call your servant Yasar (wealth), Rabah (profit), Nijih(prosperous) and Aflah (successful), for you may ask; Is he there? And someone says: No. Samurah said: These are four (names), so do not attribute more to me. (Sunan abi Dawod)
And according to what Allah says:
....So do not claim yourselves to be pure; He is most knowing of who fears Him.(53:32)
So before naming a child one should contemplate a moment whether this meaning is Ok? If I chose a name that has a certain meaning will this meaning have any impact on this child? Will this child satisfy this meaning?
How about a child having the name Barr who grows up as a heartless etc.?