"anarhcism is a heavily painted term."
It's important to pay attention when using the passive voice like this, that the actor of the verb is elided from the sentence. If you can correctly identify who is primarily responsible for 'painting' the term, you also have an explanation for why many anarchists would find your proposal as a kind of surrender, a step back, and concession to or complicity with enemies of humanity.
Historically, a lot of ideas, concepts, and movements have been renamed in order to avoid the kind of 'negative aura' you're talking about. For example, many terms considered today as offensive ableist language began as medical terms used in clinical settings several hundred years ago. Earlier terms were appropriated as slurs, and new terms were developed to replace them in a condescending manner but with the express intention of compassion. Then over time those new terms also became slurs, and the process began again. This process has been called by some the 'Euphemism Treadmill' because it doesn't stop. There is no final term that remains untainted by a 'negative aura' because the negative aura doesn't come from the term itself, but the society in which the term is used in.
The related concept of 'rebranding' is also popular in the corporate world, for example when the scandalous military contractor Blackwater rebranded to Xe, to Academi, and then to Constellis. The rebranding process requires a top-down effort which is unlikely to succeed among people with anarchist beliefs, and is usually done with the purpose of distancing the group from a significant scandal.
Anarchism as a movement is not without scandal, as with any umbrella political ideology. But it has consistently been on the right side of history, and people who proudly used 'anarchist' to identify themselves have been on the forefront of labor history, women's liberation, black power, and humanist thinking. You can't rebrand anarchism without stepping down from the shoulders of those giants who built our movement with their lives and deaths.
Anarchism is inseparable from the concept of choosing to use dysphemism over euphemism, and generally speaking plainly, truthfully, and without guile. While most of the world has moved on to using terms like 'public relations,' 'spin,' or 'fair and balanced reporting' for their self-advocacy, many anarchists embrace the old term 'propaganda' to describe their own activity. Anarchism is the opposition to what is destroying the world, and the willingness to use negatively loaded terms in a positive way is effective propaganda.
An instructive example is the history of movements and organizations fighting slavery, apartheid, discrimination, and for equal rights. Historically, these movement have had groups who accepted then-modern euphemisms for black people - for example the NAACP founded in 1909 or the UNCF in 1944, they are almost exclusively referred to by their acronyms today. There is a growing realization that conceding linguistically with the society you oppose is a form of collaboration with it.
A good counter-example is the Chicano Movement. 'Chicano' was once explicitly a racial slur, but Mexican-American leaders chose to re-appropriate the term as a positive identity. In collaboration with the Black Power movement, they fought against society's stigmatization of indigenous art, literature, and culture. They were so successful that the past associations of the term are no longer its primary association.
If you consider Zapatistas as a role model, consider this response by Subcomandante Marcos to a smear campaign by the Mexican government:
Yes, Marcos is gay. Marcos is gay in San Francisco, black in South Africa, an Asian in Europe, a Chicano in San Ysidro, an anarchist in Spain, a Palestinian in Israel, a Mayan Indian in the streets of San Cristobal, a Jew in Germany, a Gypsy in Poland, a Mohawk in Quebec, a pacifist in Bosnia, a single woman on the Metro at 10pm, a peasant without land, a gang member in the slums, an unemployed worker, an unhappy student and, of course, a Zapatista in the mountains.
You are welcome to self-identify as horizontalist here, but understand that you are not rebranding anarchism, only creating an offshoot identity that signals its willingness to co-exist with the society that structurally must suppress anarchists no matter what term they use to call themselves.