I may be fundamentally misunderstanding your question, but at least in Western Europe at the start of the period you're asking about, kingdoms already typically only had the one monarch, they just ruled much smaller kingdoms. England in the 8th Century, for example, is typically known as The Heptarchy, as there were seven main kingdoms within it: Mercia, Wessex, Kent, Essex, Sussex, East Anglia, and Northumbria. The term is commonly used to apply to Early Medieval "Anglo-Saxon" England as a whole, but this would be somewhat erroneous. Long before they coalesced into a unified England, these kingdoms were themselves the result of coalition, expansion and conquest between many smaller kingdoms.

In England, the impetus for this slow process of unification was the arrival of the Augustinian Mission to Kent in 597 and the reintroduction of Christianity, and perhaps more importantly, the re-establishment of the organised, literate hierarchy of the Church. For the majority of the pre-Christian English kingdoms, political control had been limited largely to that area which could be reached easily and quickly by the king and his retinue. Any wider territorial claims were held through nebulous terms of 'over-kingship' which essentially boiled down to "render us some tribute or I'll have to get an army together and come over there and neither of us wants that." The arrival of the literate bureaucracy of the Church allowed for a massive expansion of royal power and a commensurate expansion of territorial control. The Church allowed for the establishment of legal codexes, formalised land-holding and granting through the use of charters, the establishment of wills, writs, contracts, certified orders, estimates of land value and tax revenues and codified economic regulations. Charters, for example, allowed for kings to grant more remote lands to their subordinates but with clearly defined reciprocal terms and boundaries, expectations of rent and taxation and privileges, and well-defined geographical boundaries, and the hierarchical nature of the Church also allowed for, essentially, a 'shadow network' to keep an eye on things, and a steady expansion of royal offices and officials, which was then duplicated down the chain.

This centralisation allowed rulers to extend their power over ever-greater areas. Northumbria was unified from the kingdoms of Bernicia and Deira; Mercia's coalition structure grew to encompass kingdoms such as the Hwicce, Magonsæte, and Wæclingas, who may themselves have already been absorbed into the 'Middle Saxons' when that kingdom was absorbed into Eastern Mercia.