(1) It was good that you kept the name of new born Muhammad after azan.
(2) You may add Ahmad, Amjad, Arqam, Ahsan which you like with Muhammad. May Allah bless Muhammad with knowledge and good deed, and keep him safe from all evils, bless him with the virtues of both the worlds and give him prosperous life. Amen!
(3) Slaughter two he-goats with the intention of aqiqah and divide its meat into three parts like of that qurbani meat. Give one share to the poor and needy ones, one share to relatives and near and dear ones and keep one share for yourselves. After shaving the head rub saffron and fragrance etc on his head and give silver in charity equal to the weight of his hair or its price. The ruling of aqiqah meat is same as of qurbani.
Allah knows Best!
Darul Uloom Deoband