Toner
An Irish surname often associated with the Ó Tomhrair family, though older writers offered more than one explanation.
The #6,672 most common surname in the United States (2010 Census) — about 1 in every 60,957 Americans shares it.
Etymology
For Irish bearers, the surname is usually linked to the Gaelic family name Ó Tomhrair, which later came to be Anglicized as Toner. The older sources you provided connect it with an ancestral personal name rendered as Tomhrar/Tomhrair, though the exact linguistic history is not fully secure. The name may also be confused in some records with English-looking forms or unrelated spellings, so the Irish derivation is the safest general explanation.
History
The name is strongly associated with Ulster, especially Armagh, Londonderry, and Antrim in 19th-century Irish surname counts. Historical writers on Irish names treat Toner as an established Anglicized Irish family name rather than a recent spelling. In some older reference works, the surname was also noticed in contexts that could suggest other origins, but the Irish line is the dominant one for most modern bearers.
Origin
Regions
Variant spellings
Fun fact
One 19th-century Irish surname study places Toner among the more recognizable names of Ulster, not just as a rare spelling variant.
From the historical record
“TOMSITT TONER (Ir.) The family of O'Tomhrair, who now call themselves Toner, took their name from an ancestor 'lomhrar. — ^Joyce, Ir. Names of PI., ii. 139. TONG 1 (Eng.) Bel. to Tong or Tonge; or TONGE > Dweller at a Tongue or Point of TONGUE I Land (such, e.g., as would be formed by the meeting of two streams)…”
— Surnames of the United Kingdom: a concise etymological dictionary (2 vols in 1)