## 1 Introduction  
Processes in a distributed system must be assigned unique names to communicate and perform the required computations. Naming anonymous processes is a critical problem and is at the core of building distributed systems. The assignment of unique names to anonymous processes is known as the _naming problem_[1; 2; 3]. The naming problem is also known as an initialization protocol for ad hoc networks, where no central control or infrastructure exist. This implies the necessity of an initialization step for assigning unique names to all processes [4; 5; 6; 7; 8]. Having unique names for all processes is necessary for them to communicate and perform useful computations. In wireless communication, processes typically communicate by transmitting messages consisting of binary bits. A new topic of research was introduced in which the processes have limited communication capabilities [9]. This type of communication is known as the beeping model or beeping channels, where processes are limited to carrier sensing. Compared to messaging models, the beeping model is typically more reliable and has significantly less energy consumption [9]. Beeping channels are also known as _Beep Listen_ (BL), where a process can either listen or beep on the channel. Two models for beeping channels have been studied in which a channel can either have collision detection or not [10; 11]. We consider beeping channels without collision detection, which makes the design of naming algorithms more challenging. The beeping model received significant attention in recent years due to its simplicity and generality, which makes it applicable in many scenarios [12; 13; 14; 15]. It provides an abstraction that is appropriate for representing wireless communication networks. One of the applications of beeping model is wireless sensor networks which have grown in popularity due to the low cost of manufacturing. Many applications exist for such beeping channels in different fields such as biological sciences [16]. An example of work in this field is the development of an MIS algorithm as part of the fly's nervous system [17]. In [18; 19], ant colonies were studied in which their communication mechanism resembles a beeping channel through the perception of emitted pheromones. Existing naming algorithms were developed in [20] for single beeping channels. In [21], new energy-efficient naming algorithms were developed that minimize the number of rounds in which processes have to be active with similar time complexity of \(\mathcal{O}(n\log n)\) rounds. The limitation of communication on a single shared channel is performance bottlenecks when the number of communicating processes is high, which causes a high number of collisions. Thus, it is only natural to extend the naming of anonymous processes to multiple channels beeping model. In this paper, we consider a system of anonymous processes that communicate through multiple beeping channels. The goal is to assign unique names to all processes using a distributed algorithm. The system consists of \(N\) anonymous processes that are partitioned into \(k\) channels, such that the number of processes for channel \(j,j\in 1,2,\ldots k\), is \(n_{j}\). The strong model is assumed. Here, a process can only listen and transmit on a single channel. The communication between processes is clearly more difficult if it is carried over multiple beeping channels than a single one. The main challenge for naming in multiple beeping channels originates from the fact that processes cannot identify the source of beeps. This makes it difficult for processes in different groups to synchronize and share their knowledge about their naming compared to the single beeping channel. Moreover, the inability to detect collisions further complicates the design of the naming algorithms. We developed two novel naming algorithms for assigning unique names to anonymous processes for the models where the number of processes is either known or unknown, respectively.