If genetic testing proves that a specific guy is the biological father of my child does that mean the child would automatically bear his surname?

No! Where the mother is single the child automatically bears the mother's name and will only bear the  father's surname instead, or bear the surname of both parents, if there is mutual consent.

If the mother is married, and as a rare exception, the Israeli court allows and orders D.N.A testing to be carried out , to establish paternity of a child born to her, where there is no religious prohibtion to this, then the child's surname ( family name)  will remain the mother's married name, even if it is the same as her husband's surname, and the testing proves that her husband is not the minor's biological father, but a third party, who impregnated the mother, is the minor's biological father.

Usually paternity testing is refused in Israel where the mother is married, but it may be ordered in exceptional conditions, and especially if there is no religious bar - for example if the mother is Jewish, but her husband is non-Jewish.

Following Israeli family court proceedings,  in March 2017 the Ministry of Interior was ordered  to register the paternity of  a child born as a result of an extra-marital affair between the Jewish mother,( married to a non-Jew), and a single non-Jewish man, but the child's surname remained the mother's married surname.