There are combinations like sugar mugar that people use in their speech while the second word has no meaning and only adds a rhythm. What is this called in English?
In linguistics, this sort of repetition is called reduplication, and the second half is sometimes called a reduplicant. Reduplication is the most common term, but let's explore some more specific terms that are less common.
In your example, the reduplicant is altered, incorporating a special kind of prefix, and although there is no common term for this, a few linguists have called this a duplifix:
If we adopt this terminology, one common example would be the English duplifix (prefix) /ʃm/ (variously spelled shm or schm), and this process is sometimes called shm-reduplication. This particular duplifix is used to express a pejorative attitude toward the discourse topic – skepticism, dismissal, or similar sentiments:
Here, breakfast is the discourse topic, and Brodie is expressing a pejorative, dismissive attitude toward this topic with shm-reduplication.
More generally, this category of reduplication is also known as echo reduplication, and this occurs in many languages. In your example, mugar echoes sugar, but with the initial consonant replaced with /m/. This might be the best term for your particular example; it doesn't imply any sort of pejorative meaning like shm-reduplication does.