Peace be with you,
Congratulations to you and your family on this wonderful news. May our Lord grant him a righteous and healthy life, God willing.
There are no restrictions on names as long as they are nice names and do not have contestable meanings.
[1] ‘Ammar’ in its primary sense means to live or continue in life for a long time. Obviously this is something for God to decide so giving a child that name may have some connotations to it (as a statement of fact) which you may want to consider in light of verse 35.11. Similarly,
'Rahman' on its own may carry a connotation which may be better advised to avoid especially when God has used the Arabic expression for Himself.
017:110“Say: "Call upon Allah, or call upon Rahman: by whatever name ye call upon Him, (it is well): for to Him belong the most beautiful names. Neither speak thy Prayer aloud, nor speak it in a low tone, but seek a middle course between."” The action of shaving the baby's hair, circumcision
[2], Aqiqa, etc are all cultural expressions often given religious decree. They have no explicit basis in the Quran. Of course, there is no harm in following such rituals as long as one doesn't claim them to be
'religiously ordained'. Some rituals such as circumcision may even have health / medical benefits.
Regards,
Joseph.
RELATED ARTICLES[1] WHAT IS A MUSLIM NAME? - A MISNOMERhttp://quransmessage.com/articles/muslim%20name%20FM3.htm[2] CIRCUMCISIONhttp://quransmessage.com/articles/circumcision%20FM3.htm