وَمَنْ يُعَظِّمْ شَعَائِرَ اللَّهِ فَإِنَّهَا مِنْ تَقْوَى الْقُلُوبِ
And whoever venerates that which Allah has sanctified, it is certainly from the piety of hearts. (Surah al-Haj, 22).
If the name is at the place of Sajdah, then this is something which is best avoided. However, if it is elsewhere like in the corner, then in itself there is no issue with it unless your name contains the name of Allah (Most High), such as Abdullah, Abd al-Rahmaan or something else that we hold to be sacred (e.g. names of prophets). In this case it may be considered to be a lack of Adab and thus Makruh. Some Hanafi scholars mentioned that it is Makruh to spread a sheet on the ground if it contains the name of Allah (Most High).
بِسَاطٌ أَوْ غَيْرُهُ كُتِبَ عَلَيْهِ الْمُلْكُ لِلَّهِ يُكْرَهُ بَسْطُهُ وَاسْتِعْمَالُهُ إلَّا إذَا عُلِّقَ لِلزِّينَةِ يَنْبَغِي أَنْ لَا يُكْرَهَ
It is Makruh to spread or use a sheet or the like that has ‘the dominion is for Allah’ written on it. However it if it is hung up for the purpose of beautification then it should not be considered Makruh. (Imam Ibn Nujaym, al-Bahr al-Raiq).
Although this maybe open to opinion and interpretation if one has his own name on the floor, which happens to contain the Holy Name of Allah (Most High), it is still best avoided since the Dhahir (apparent) meaning of the text will include this within the Karahah (dislike).
If such a name were to be written close to the feet on the prayer mat (Musalah, Sajadah) then it is clearly disrespectful and thus prohibited, so must be avoided.
And Allah (Most High) Knows best.
– Answered by Shaykh Noorud-deen (09.02.2021)