First I need to apologize for my former comments based on a misunderstanding and need for clarification at my first reading of your post. The comment of UmH actually brought some light into this darkness.
Secondly in fact أرحم (Arham) in Arabic might be a superlative or simply a verb of comparison between two entities and their mercy towards others. And anything that is comparable can hardly be Devine only so naming a child Arham is certainly permissible. It means merciful (than) or in case there's a clear link to Allah most merciful.
Thirdly - and this is rather off-topic- I'd avoid naming a child this name (because of the above ambiguity and the existence of better choices) and prefer using names our prophet () recommend names that include the meaning of thankfulness (hamd) and worship (names with prefix 'Abdu), the next good choice are names of prophets () and faithful people (for example sahabah etc.).
As for what you referred to as direct and indirect names:
I think what you mean are those combined names based on the prefix 'Abdu + name or attribute of Allah.
Let me tell you that عبد أرحم sounds more than weird for an Arabic speaker as Arham is either a verb requiring a noun on which it applies or an adjective so it requires in both cases a noun starting with the necessary letters ( ال) or an explaining sentence that may replace such a noun in the Arabic grammar.
Be aware that among all names and attributes of Allah only two are haram for direct use for humans and they are part of the basmalah:
Bismi-l-Lahi ar-Rahmani ar-Rahim
There's no need to explain that one of this two is the name Allah الله itself. You may call a child worshiper of Allah ('Abdullah عبد الله) which certainly is an adequate name. It falls under the above category of names including the meaning of worship.
As for ar-Rahman (الرحمان، الرحمن) it refers to "the all and extensively and most Merciful (without limitation or exclusions) ".
While ar-Rahim ( الرحيم) refers to "the most (but exclusively) Merciful with believers".
I think it is now clear that calling a person ar-Rahman is haram.
On the other hand any body could be ar-Rahim under certain conditions and if we lift the letters (ال) from an Arabic name we take of th
To Be Contonued