I need to create a name for my products; this name will concatenate the values found into 2 or 3 others that already exist: product.name (standard Odoo) + personalized fields.

A solution was given for a different environment: see 

Merging fields into one

Specifically the Saas environment does't allow to create a new field with the function option.

Any direction will be appreciated

UPDATE :

(I tested the following configuration having created 2 fields x_nomcomplet and x_auteur type char on modèle product template modèle d'article)

remove previous server action and create 2 new records with values for fields of server action :

first (for field Action name you can choose what you want):

Action name : Nom complet article

Base Model : Modèle d'article

Action To Do : Execute python code

condition : True

Sequence : 5

notebook python code, add following code:

context = context or {}

for record in self.browse(cr, uid, context.get('active_ids', []), context=context):

    value = ""

    for val in [record.name, record.x_auteur]:

        if val:

            value += "%s " % val

    pool.get('product.template').write(cr, uid, record.id, {'x_nomcomplet': value[:-1]}, context=context)

at the top right of the form push button "Add in the More menu" (will add buttons to tree and form of the menu product)

second (for field Action name you can choose what you want):

Action name : Nom complet variante

Base Model : Article

Action To Do : Execute python code

condition : True

Sequence : 5

notebook python code, add following code:

context = context or {}

for record in self.browse(cr, uid, context.get('active_ids', []), context=context):

    value = ""

    for val in [record.product_tmpl_id.name, record.product_tmpl_id.x_auteur]:

        if val:

            value += "%s " % val

pool.get('product.template').write(cr, uid, record.product_tmpl_id.id, {'x_nomcomplet': value[:-1]}, context=context)

at the top right of the form push button "Add in the More menu" (will add buttons to tree and form of the menu product variant)

test in menus product and variant