Ó Cléirchín
You don't. Cheyenne is a non-Gaelic, proper name and, as such, has no Gaelic spelling.
The closest Gaelic name is Aidan, spelled Aodhán in Irish Gaelicand Aodhan in Scottish Gaelic.
The Scottish Gaelic form of the surname is MacIllFhionndaig.As a first name it would be Liondsaidh.(Some Irish families that adopted the name 'Lindsay' were MacClintock, Lynchy, and O'Lynn.)
There is no special Gaelic form of the name; it would be the same.
A rose (flower) is rós in Irish;the name Rose is Róisín (a diminutive) in Irish.Scottish Gaelic: ?
This sort of name is left in the original form even if the last name is in an Irish Gaelic or Scottish Gaelic form.
In Irish it's "de Fuitnigh". This is a lastname, not a given name.
'On occasion the Irish name Béibhinn has been wrongly anglicized Vivian.'
There is no Irish equivalent for the French name.
The name Eamonn is Irish (Gaelic) for Edmund. If you spell the name with one 'e' then it means Edward.
The Irish Gaelic name Somhairle (Sorley) is equated with Samuel; also true for the Scottish Gaelic version Somhairle. It derives from the Norse Summarliethi/Somerled rather than Samuel.
Scottish: Calum the Irish equivalent is Colm (pronounced kullum).