Looking at NCIS fanfic will give you a specific feel to how Ducky speaks. "Anthony" this and "Abigail" that. Reading that a person would assume that this is accurate to how Ducky talks in canon.
But you would be wrong.
Flipping channels the other day I caught the beginning of "Twisted Sister." When approaching the team Ducky apologizes for not being there earlier due to problems parking the van and then says "I would have thought McGee would have beaten me up here." McGee. Not Timothy.
That made me curious. I hunted down transcripts and started researching what Ducky called the various team members, as well as the guest stars. The incident in "Twisted Sister" had to be the anomaly, right?
Actually, according to all the transcripts I could find (S1-4, for a total of 84 episodes. Statistics from Brothers in Arms, In the Dark, Trojan Horse, Angel of Death and Model Behavior are from watching the episodes, not transcripts) the answer is, for the most part, no.
He mentions names in the following manner:
Jethro: 145 vs Gibbs: 52 (also Leroy Jethro Gibbs: 3, Special Agent Gibbs:3, and Agent Gibbs: 7, 'Director':1)
Mister Palmer: 122 vs Jimmy: 7
Abby: 85 vs Abigail: 8 vs Miss Sciuto: 1
Tony: 41 vs DiNozzo: 3 vs Anthony:1 vs Anthony DiNozzo: 1
Gerald: 32
Kate: 17 vs Caitlin: 12
Timothy: 18 vs McGee: 9
Ziva: 14 vs Officer David: 3
Director: 3 vs the Director: 4
Christopher: 2 vs Chris:1 vs Christopher Pacci:1
Agent Lee: 3
Dennis:1, Elmo: 2, Agent Fuller: 1, Agent Burley: 1, Digger: 4, Charlie:1
Cassie: 2, Janice: 3, Sandy: 1, Yost: 2, Mister Yost: 1, Ari: 4, Tobias: 1, Shannon & Kelly: 1, Rick: 2, Agent Cassidy: 2, Sharif:2. Sheriff: 1, Monsieur Grenouille: 1 (while undercover), Renee: 1, Jackson Scott: 1
Other than Kate and Pacci the victims are always referred to by their rank or a combination of their rank and last name.
It's interesting that Gerald is always Gerald, yet Jimmy is nearly always Mister Palmer. And remembering that Jimmy is in a lot fewer episodes than the other characters his name is used by Ducky a significant number of times.
Occasionally full names were used in jest. Gibbs calling him Doctor (and stressing the word) resulted in one of the uses of Special Agent Gibbs. Abby, after his first use of Abigail asks him not to call her that and the next time he does she replies, "Donald."
I'll admit that early seasons are not always indicative of later ones, but I found the breakdown of his usage of people's names interesting and thought other people might as well. (If there is interest I can post the breakdown by episode and season as well)
edited to add- I was curious, so I went through the subtitles for uses of "Anthony" even though it's difficult to ascertain who said what. "Anthony" is not used in the S3 and S4 episodes missing transcripts. For S5 and S6, other than what seems to be Tony introducing himself, it appears that Ducky calls him Anthony 6 times: once in "Stakeout," twice in "Cloak" and "Bounce" and once in "Semper Fidelis." (No "young Anthony" uses however.)