It is narrated from Nafi' that when Abdullah bin Umar (may Allah be pleased with them both) began the recitation in prayer, he would recite 'Bismillahir-Rahmanir-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful). Then, when he finished Surah al-Fatihah, he would also recite 'Bismillah' (In the name of Allah) when beginning the next surah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3057
Nafi' narrates from Sayyiduna Ibn Umar (may Allah be pleased with them both) that when Sayyiduna Ibn Umar (may Allah be pleased with them both) recited, he would recite "In the name of Allah, the Most Gracious, the Most Merciful" [Surah al-Fatihah: 1] aloud, and when he recited the next surah he would again recite the Bismillah aloud.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3058
It is narrated from Azraq bin Qays: I prayed behind Ibn al-Zubayr (may Allah be pleased with them both). He would recite 'Bismillahir-Rahmanir-Rahim' (In the name of Allah, the Most Gracious, the Most Merciful), and then, when he recited "nor of those who have gone astray" [Surah al-Fatihah: 7], he would again recite 'Bismillahir-Rahmanir-Rahim'.
This has been narrated to us from Abu Hurayrah (may Allah be pleased with him) and several other Companions (may Allah be pleased with them).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3059