Are Taha and Yaseen names of the Prophet (blessings and peace of Allah be upon him)?

Taha and Yaseen are not names of the Prophet (blessings and
peace of Allah be upon him); rather they are among the separate letters that
appear at the beginning of some soorahs of the Holy Qur’aan, which point to
the miraculous nature of the Qur’aan and the fact that these letters are
part of the language of the Arabs, yet despite that they were unable to
produce anything like it, which indicates that it was revealed from Allah,
may He be exalted. 

Muhammad al-Ameen ash-Shanqeeti (may Allah have mercy on him)
said in Adwa’ al-Bayaan
(4/3), commenting on Soorah Ta-Ha: 

The most correct opinion concerning it in my view is that
these are the separate letters that appear at the beginning of some soorahs.
What may prove that is the fact that the ta’ and ha’ that appear at the
beginning of this soorah also appear in other places in which there is no
dispute that they are among these separate letters. The letter ta’ appears
at the beginning of ash-Shu‘ara’ (Soorah 26), “Ta Seen Meem”; and at the
beginning of an-Naml (Soorah 27), Ta’ Seen, and at the beginning of as-Qasas
(soorah 28). As for the letter ha’, it appears at the beginning of Soorat
Maryam where Allah, may He be exalted, says “Kaaf Ha’ Yaa ‘Ayn Saad.” End
quote. 

Shaykh as-Sa‘di (may Allah have mercy on him) said in his
Tafseer (1/501): “Ta-Ha” is one of the separate letters with which many
soorahs begin, and it is not one of the names of the Prophet (blessings and
peace of Allah be upon him). End quote. 

Shaykh Ibn Baaz (may Allah have mercy on him) said: Taha and
Yaseen are not names of the Prophet (blessings and peace of Allah be upon
him) according to the more correct of the two scholarly opinions; rather
these are some of the separate letters that appear at the beginning of some
soorahs, such as saad, qaaf, noon and so on.

End quote from Majmoo‘ al-Fataawa, 18/54 

And Allah knows best.