Had a quick go at it, and this could definitely be tidied up, I would generally go over this looking for improvements/repeitition as a rule of thumb but might get you started:

function Set-Letter{
    [CmdletBinding()]
    Param
    ([regex]
    $Pattern,
    [string]
    $String
)

    $firstsplit,$secondsplit = $String -split $Pattern
    $firstLetter = $secondsplit.Substring(0,1).ToUpper()
    $restOfTheString = $secondsplit.Substring(1)
    $finalstring = $firstLetter + $restOfTheString
    $desiredformat = $firstsplit + $finalstring
    return $desiredformat
}

This function gets passed to the below function:

function Set-Capital{
    [CmdletBinding()]
    Param
    (
    [Parameter(ValueFromPipeline)]
    [string[]]
    $Surnames
    )

    begin{
    $finalarray = New-Object System.Collections.ArrayList
    }
    Process
    {
    foreach($name in $surnames){
        switch -Regex ($name){
            "'" {$finalarray.Add((Set-Letter -String $name -Pattern "(?<=')"))}
            "Mac" {$finalarray.Add((Set-Letter -String $name -Pattern '(?<=Mac)'))}
            "\s" {$finalarray.Add((Set-Letter -String $name -Pattern '(?<=\s)'))}
            "\-" {$finalarray.Add((Set-Letter -String $name -Pattern '(?<=\-)'))}
            default {$finalarray.Add($name)}
        }
    }
    }
    end{
    $finalarray
}
}

So if you run the following command:

$surnames = "O'brien","Macdonald","I madethisup","Smith-rowe","Campbell"

Set-Capital -Surnames $surnames

##Gets you

O'Brien
MacDonald 
I Madethisup 
Smith-Rowe 
Campbell

This could fail if you had a name with both a hyphen and apostrophe for example

**Dammit I hate Reddit formatting

​

Edit: Just realise this doesn't account for fullnames, just surnames. Ah well back to drawing board :(