"Walid" (ولید) means "a newborn child", while "Rahman" (رحمان) is one of the attributes of Allah the Almighty. Together, "Walid al-Rahman" means "the newborn child of Rahman". This meaning amounts to kufr [disbelief], because Allah the Almighty is free from and above having children.
Therefore, it is not permissible to use the name "Walid al-Rahman". In its place, names such as Muhammad Walid (محمد ولید) or Walid Ahmad (ولید احمد) should be used.
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.
القرآن الکریم: (الاخلاص)
قُلْ هُوَ اللَّهُ أَحَدٌo اللَّهُ الصَّمَدُo لَمْ يَلِدْ وَلَمْ يُولَدْo وَلَمْ يَكُنْ لَهُ كُفُوًا أَحَدٌo
القاموس الوحید: (ص: 1481، ط: ادارة اسلامیات)