Golff y Côd - Treiglad

JavaScript (ES6), 180 bytes

x=>x.replace(/^([cpt](?!h)|d(?!d)|[bgm]|ll|rh)(.+)/,(_,y,z)=>({p:"b mh ph",t:"d nh th",c:"g ngh ch",b:"f m",d:"dd n",g:" ng",m:"f"}[y]||y[0]).split` `.map(b=>a.push(b+z)),a=[x])&&a

Outputs as an array of strings. This is my first try, so it's almost certainly not optimal.

Try it out

f=x=>x.replace(/^([cpt](?!h)|d(?!d)|[bgm]|ll|rh)(.+)/,(_,y,z)=>({p:"b mh ph",t:"d nh th",c:"g ngh ch",b:"f m",d:"dd n",g:" ng",m:"f"}[y]||y[0]).split` `.map(b=>a.push(b+z)),a=[x])&&a

<input id=A value="pobl"><button onclick="B.innerHTML=f(A.value).join('<br>')">Run</button><br>
<pre id=B>

C#, 356 338 360 bytes

I know that C# is a poor choice for code golf, but it's worth the shot:

Third attempt, all cases now pass, including th- ph- etc. This adjustment cost roughly 18 bytes.

Thanks pinkfloydx33 for the tips saving 24 bytes!

namespace System{using Linq;using S=String;class P{static void Main(S[]a){Action<S>w=Console.WriteLine;w(a[0]);foreach(S r in"th-dd-ch-ph-p.b.mh.ph-t.d.nh.th-c.g.ngh.ch-b.f.m-d.dd.n-g..ng-m.f-ll.l-rh.r".Split('-')){var b=r.Split('.');if(a[0].StartsWith(b[0])){foreach(S f in b.Skip(1))w(Text.RegularExpressions.Regex.Replace(a[0],$"^{b[0]}",f));break;}}}}}

Output

$> ./p gwernymynydd
gwernymynydd
wernymynydd
ngwernymynydd

Formatted Version

    namespace System {
    using Linq;
    using S = String;

    class P {
        static void Main(S[] a) {
            Action<S> w = Console.WriteLine;
            w(a[0]);
            foreach (S r in "th-dd-ch-ph-p.b.mh.ph-t.d.nh.th-c.g.ngh.ch-b.f.m-d.dd.n-g..ng-m.f-ll.l-rh.r"
                .Split('-')) {
                var b = r.Split('.');
                if (a[0].StartsWith(b[0])) {
                    foreach (S f in b.Skip(1))
                        w(Text.RegularExpressions.Regex.Replace(a[0], $"^{b[0]}", f));
                    break;
                }
            }
        }
    }
}

PowerShell v3+, 254 231 bytes

param($a)$a;$z=-join$a[1..$a.length]
if(($x=@{112='b mh ph';116='d nh th';99='g ngh ch';98='f m';100='dd n';109='f'})[+$a[0]]-and$a-notmatch'^[cpt]h|^dd'){-split$x[+$a[0]]|%{"$_$z"}}
($z,"ng$z")*($a[0]-eq103)
$z*($a-match'^ll|^rh')

working to golf further...

Examples

(Output is space-separated because that's the default Output Field Separator for stringified arrays. I don't know if the words I used for testing are actual words, but they fit the exceptions.)

PS C:\Tools\Scripts\golfing> 'dydd','pobl','gwernymynydd','ffrindiau','enw','rhee','llewyn','chern','ddydd','phobl'|%{"$_ --> "+(.\golff-yr-cod.ps1 $_)}
dydd --> dydd ddydd nydd
pobl --> pobl bobl mhobl phobl
gwernymynydd --> gwernymynydd wernymynydd ngwernymynydd
ffrindiau --> ffrindiau
enw --> enw
rhee --> rhee hee
llewyn --> llewyn lewyn
chern --> chern
ddydd --> ddydd
phobl --> phobl