tolkiens legendarium - Did Elrond Half-Elven have any title?

Elrond is clearly in charge at Rivendell, and is an important and powerful person in the world at large. He is a ring-bearer, having received Vilya from his great-uncle Gil-galad. He also held a position of command in Gil-galad's army. He is of royal descent. His brother Elros Tar-Minyatur was the first king of Númenor. And yet Elrond himself seems to have no title at all.

"Half-Elven" serves more as a descriptor than a title. He is also known as the master of Imaldris, but that too seems to be a description, not a title as such. He is never, to my memory, addressed as Master.

Answer

Yes, he was the Lord of Rivendell

The face of Elrond was ageless, neither old nor young, though in it was written the memory of many things both glad and sorrowful. His hair was dark as the shadows of twilight, and upon it was set a circlet of silver; his eyes were grey as a clear evening, and in them was a light like the light of stars. Venerable he seemed as a king crowned with many winters, and yet hale as a tried warrior in the fullness of his strength. He was the Lord of Rivendell and mighty among both Elves and Men. - _{^{FOTR : Chapter 1 - Many Meetings}}

We are advised in the Unfinished Tales that he was appointed as Gil-galad's vice-regent in Eriador.

At this time the first Council was held, and it was there determined that an Elvish stronghold in the east of Eriador should be maintained at Imladris rather than in Eregion. At that time also Gil-galad gave Vilya, the Blue Ring, to Elrond, and appointed him to be his vice-regent in Eriador; but the Red Ring he kept, until he gave it to Círdan when he set out from Lindon in the days of the Last Alliance.

And he also served as the herald of Gil-galad during the War of the Ring.

`I was the herald of Gil-galad and marched with his host. I was at the Battle of Dagorlad before the Black Gate of Mordor, where we had the mastery: for the Spear of Gil-galad and the Sword of Elendil, Aiglos and Narsil, none could withstand. _{^{FOTR : Chapter 2 - The Council of Elrond}}

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The Silmarillion has some other (informal) titles for him; "master of Imladris" (note the lack of capitalisation) and "keeper of Vilya, the Ring of Air" as well as Master Elrond and Elrond Half-elven which is, as you've noted more of a descriptor:

Elrond Son of Eärendil and Elwing, who at the end of the First Age chose to belong to the Firstborn, and remained in Middle-earth until the end of the Third Age; master of Imladris (Rivendell) and keeper of Vilya, the Ring of Air, which he had received from Gil-galad. Called Master Elrond and Elrond Half-elven

Frodo, in Two Towers describes him as "Elrond of Imladris"

My part in the Company was known to him, as to all the others. for it was appointed to me by Elrond of Imladris himself before the whole Council. On that errand I came into this country, but it is not mine to reveal to any outside the Company.

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For the record, he is repeatedly called "Master Elrond" by the various members of the Fellowship including Frodo, Boromir and Gandalf:

'And let us hope that none will ever speak it here again,' answered Gandalf. 'Nonetheless I do not ask your pardon, Master Elrond.