Were the Gospels originally written anonymously? And if they were, how, when and where were they altered?Who assigned the gospel authors originally?

According to the theory of the originally anonymous gospels, the titles of the most ancient surviving manuscripts were added later on. I would like to know: **For each gospel, how many different, distinct, "assigners" were there? When did they do the assignment and where were they?** I am not asking about the authorship of the gospels, but supposing there were no titles, **who** assigned them. For example: **The gospel according to Matthew was assigned by:** 1) X1 person or group, in the Y century in the Z region. 2) X2 person or group, ..."" If much of this is not possible at least list the number of the different assigners and whether they may have assigned these texts independently of one another. **The gospel according to Luke... ""** Please give sources, thank you!