Primary alcohols have been an active area of research since the beginning of the 20th century. The main problem in studying monohydroxy alcohols is the molecular origin of the slower Debye relaxation, whereas the faster process, recognized as structural relaxation, remains much less investigated. This is because in many primary alcohols the structural process is strongly overlapped by the dominating Debye relaxation. Additionally, there is still no answer for many fundamental questions concerning the origin of the molecular characteristic properties of these materials. One of them is the role of molecular architecture in the formation of hydrogen-bonded structures and its potential connection to the relaxation dynamics of Debye and structural relaxation processes. In this article, we present the results of ambient and high-pressure dielectric studies of monohydroxy alcohols with similar chemical structures but different carbon chain lengths (2-ethyl-1-butanol and 2-ethyl-1-hexanol) and positions of the OH- group (2-methyl-2-hexanol and 2-methyl-3-hexanol). New data are compared with previously collected results for 5-methyl-2-hexanol. We note that differences in molecular architecture have a significant influence on the formation of hydrogen-bonded structures, which is reflected in the behavior of the Debye and structural relaxation processes. Intriguingly, studying the relaxation dynamics in monohydroxy alcohols at high pressures of up to p = 1700 MPa delivers a fundamental bridge to understand the potential connection between molecular conformation and its response to the characteristic properties of these materials.