Actually, I think this is one issue where consistency may hurt your writing. Both are acceptable, and which one you choose is often a matter of emphasis:
"X said" tends to put emphasis on "said" (or the corresponding verb). It makes the speaker inconspicuous. Personally, I'd use this if the name is just there as a reminder. That's why "said [pronoun]" often sounds strange, I think. A pronoun refers back to a name/noun given earlier, so there's rarely a reason to put it into a prominent position.
"said [name]" for example is often appropriate when introducing "surprising speakers".
"No, you're not!" said Mom.//I flinched, turning...
If Mom hasn't been in the scene before, "Mom said" sounds awkward, I think. And notice that even a pronoun would work in that place, if it was clear who the pronoun referred to:
"Him..."//"Who?"//"You know. Him!"//"Oh!"
[snip]
"No, you're not!" said he.//I froze, lowered my head, hoping to hide my blush.
Starting sentences with "Said [X]" doesn't sound right to me (except in rather archaic/poetic contexts), which makes consistency kind of hard for people who prefer the structure.
To summarize:
1. At the start of the sentence/before the quote: X said, "..."
2. To emphasize the speaker: "...," said X.
3. To emphasize the speaking: "...," X said.
4. With pronouns: "...," [pronoun] said. (Unless 2. applies, but it usually won't. If you wish to the emphasise the speaker, you're not usually using a pronoun.)
That's my take on it, in a nutshell. As always, writing is more complicated.