The prayer of a person who does not perform ablution is invalid, and the ablution of a person who does not mention the name of Allah is invalid
Authentic hadithعن أبي هريرة، قال: قال رسول الله صلى الله عليه وسلم : «لا صلاةَ لِمن لا وُضوءَ له، ولا وُضوءَ لِمن لم يَذْكر اسم الله تعالى عليه».
Abu Hurayrah reported that the Messenger of Allah (may Allah's peace and blessings be upon him) said: "The prayer of a person who does not perform ablution is invalid, and the ablution of a person who does not mention the name of Allah is invalid."
Explanation
Abu Hurayrah (may Allah be pleased with him) reported that the Messenger of Allah (may Alla's peace and blessings be upon him) judged the prayer of a person who did not perform ablution to be invalid, and so is the ablution of a person who did not mention the name of Allah at its start. The Hadīth clearly states that that it is compulsory to mention Allah's name when beginning ablution. Therefore, intentionally leaving it invalidates one's ablution. However, leaving it out of ignorance or forgetfulness does not invalidate it.
Source · Narrated by Ibn Majah - Narrated by Abu Daoud - Narrated by Ahmad
From the Hadith Encyclopedia (hadeethenc.com).