Someone didn't read this manga properly.
The naming of an Imae demon is a highly valued and sacred practice within the Imae demon tribe culture, and is normally done by the tribe elder/leader. Not being bestowed a name is usually associated with being cast out of the tribe and deliberately being ostracized and shunned by your own kind- this is what happened to MC as a result of his mother marrying a human. The 2nd ML was trying to give him the blessing of having a name, which is what MC's mother never got to do (she finally planned to defy the elder and name her son herself, but was killed before she had the chance.)
The 2nd ML knows MC's tragic backstory, and wanted to bring him happiness and belonging by finally giving him a name. His "obsession" is genuine love and is also to make MC finally feel loved, cherished, and valued after all the cruelty that he was forced to suffer in the world since birth. MC doesn't want to accept 2nd ML's affection out of fear he may accidentally hurt or kill him with his demon blood's poison traits.
Bro it is SO clearly VISIBLE that the MC FEAAAAARS both of these characters, one is fucking crazy the other is obsessed with the thought of 'naming' the mc as if he's a fucking possession. UGHHHHHHヽ(`Д´)ﾉ