Dude you cant rebrand hawiyenimo.Hawiye clan formation is similar to the arab clan formation,
After the collapse of Ajuran Empire, those who had a common lineage(hawiye)have continued following the same system.
Ajuran Controlled all the Way to KISMAYO
View attachment 257390
Some of the groups you mentioned are non-hawiye but a samaale group aka the pre-hawiyes but joined hawiye politically. Which is why some of them Have hawiye seats.
Some Sheikhals, particularly the Aw Axmed Loobage subclan, claim they are part of Hiraab which in turn is part of the larger Hawiye group, while others, such as the Aw-Qutub subclan, dispute this.
You are more of like Italians claimming the magestic roman empire.
When hawiye claim ajuran.